Annals of Pure and Applied Logic最新文献

英文中文

Ordered transexponential fields

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-12-02 DOI: 10.1016/j.apal.2024.103541

Lothar Sebastian Krapp , Salma Kuhlmann

We develop a first-order theory of ordered transexponential fields in the language

{+, \cdot, 0, 1, <, e, T}

, where e and T stand for unary function symbols. While the archimedean models of this theory are readily described, the study of the non-archimedean models leads to a systematic examination of the induced structure on the residue field and the value group under the natural valuation. We establish necessary and sufficient conditions on the value group of an ordered exponential field

(K, e)

to admit a transexponential function T compatible with e. Moreover, we give a full characterisation of all countable ordered transexponential fields in terms of their valuation theoretic invariants.

引用次数: 0

Tame topology in Hensel minimal structures

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-29 DOI: 10.1016/j.apal.2024.103540

Krzysztof Jan Nowak

We are concerned with topology of Hensel minimal structures on non-trivially valued fields K, whose axiomatic theory was introduced in a recent paper by Cluckers–Halupczok–Rideau. We additionally require that every definable subset in the imaginary sort RV, binding together the residue field Kv and value group vK, be already definable in the plain valued field language. This condition is satisfied by several classical tame structures on Henselian fields, including Henselian fields with analytic structure, V-minimal fields, and polynomially bounded o-minimal structures with a convex subring. In this article, we establish many results concerning definable functions and sets. These are, among others, existence of the limit for definable functions of one variable, a closedness theorem, several non-Archimedean versions of the Łojasiewicz inequalities, an embedding theorem for regular definable spaces, and the definable ultranormality and ultraparacompactness of definable Hausdorff LC-spaces.

引用次数: 0

Strength and limitations of Sherali-Adams and Nullstellensatz proof systems

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-28 DOI: 10.1016/j.apal.2024.103538

Ilario Bonacina, Maria Luisa Bonet

We compare the strength of the algebraic proof systems Sherali-Adams (

SA

) and Nullstellensatz (

NS

) with Frege-style proof systems. Unlike bounded-depth Frege,

SA

has polynomial-size proofs of the pigeonhole principle (PHP). A natural question is whether adding PHP to bounded-depth Frege is enough to simulate

SA

. We show that

SA

, with unary integer coefficients, lies strictly between tree-like depth-1

Frege + PHP

and tree-like

Resolution

. We introduce a levelled version of PHP (

L PHP

) and we show that

SA

with integer coefficients lies strictly between tree-like depth-1

Frege + L PHP

and

Resolution

. Analogous results are shown for

NS

using the bijective (i.e. onto and functional) pigeonhole principle and a leveled version of it.

{"title":"Strength and limitations of Sherali-Adams and Nullstellensatz proof systems","authors":"Ilario Bonacina, Maria Luisa Bonet","doi":"10.1016/j.apal.2024.103538","DOIUrl":"10.1016/j.apal.2024.103538","url":null,"abstract":"<div><div>We compare the strength of the algebraic proof systems Sherali-Adams (<span><math><mi>SA</mi></math></span>) and Nullstellensatz (<span><math><mi>NS</mi></math></span>) with Frege-style proof systems. Unlike bounded-depth Frege, <span><math><mi>SA</mi></math></span> has polynomial-size proofs of the pigeonhole principle (<span>PHP</span>). A natural question is whether adding <span>PHP</span> to bounded-depth Frege is enough to simulate <span><math><mi>SA</mi></math></span>. We show that <span><math><mi>SA</mi></math></span>, with unary integer coefficients, lies strictly between tree-like depth-1 <span><math><mtext>Frege</mtext><mo>+</mo><mrow><mi>PHP</mi></mrow></math></span> and tree-like <span><math><mtext>Resolution</mtext></math></span>. We introduce a <em>levelled</em> version of <span>PHP</span> (<span><math><mi>L</mi><mrow><mi>PHP</mi></mrow></math></span>) and we show that <span><math><mi>SA</mi></math></span> with integer coefficients lies strictly between tree-like depth-1 <span><math><mtext>Frege</mtext><mo>+</mo><mi>L</mi><mrow><mi>PHP</mi></mrow></math></span> and <span><math><mtext>Resolution</mtext></math></span>. Analogous results are shown for <span><math><mi>NS</mi></math></span> using the bijective (i.e. onto and functional) pigeonhole principle and a leveled version of it.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 4","pages":"Article 103538"},"PeriodicalIF":0.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

More about the cofinality and the covering of the ideal of strong measure zero sets

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-28 DOI: 10.1016/j.apal.2024.103537

Miguel A. Cardona , Diego A. Mejía

We improve the previous work of Yorioka and the first author about the combinatorics of the ideal

SN

of strong measure zero sets of reals. We refine the notions of dominating systems of the first author and introduce the new combinatorial principle

DS (δ)

that helps to find simple conditions to deduce

d_{κ} \leq cof (SN)

(where

d_{κ}

is the dominating number on

κ^{κ}

). In addition, we find a new upper bound of

cof (SN)

by using products of relational systems and cardinal characteristics associated with Yorioka ideals.

In addition, we dissect and generalize results from Pawlikowski to force upper bounds of the covering of

SN

, particularly for finite support iterations of precaliber posets.

Finally, as applications of our main theorems, we prove consistency results about the cardinal characteristics associated with

SN

and the principle

DS (δ)

. For example, we show that

cov (SN) < non (SN) = c < cof (SN)

holds in Cohen model, and we refine a result (and the proof) of the first author about the consistency of

cov (SN) < non (SN) < cof (SN)

, with

c

in any desired position with respect to

cof (SN)

, and the improvement that

non (SN)

can be singular here.

{"title":"More about the cofinality and the covering of the ideal of strong measure zero sets","authors":"Miguel A. Cardona , Diego A. Mejía","doi":"10.1016/j.apal.2024.103537","DOIUrl":"10.1016/j.apal.2024.103537","url":null,"abstract":"<div><div>We improve the previous work of Yorioka and the first author about the combinatorics of the ideal <span><math><mi>SN</mi></math></span> of strong measure zero sets of reals. We refine the notions of dominating systems of the first author and introduce the new combinatorial principle <span><math><mrow><mi>DS</mi></mrow><mo>(</mo><mi>δ</mi><mo>)</mo></math></span> that helps to find simple conditions to deduce <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>κ</mi></mrow></msub><mo>≤</mo><mrow><mi>cof</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo></math></span> (where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>κ</mi></mrow></msub></math></span> is the dominating number on <span><math><msup><mrow><mi>κ</mi></mrow><mrow><mi>κ</mi></mrow></msup></math></span>). In addition, we find a new upper bound of <span><math><mrow><mi>cof</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo></math></span> by using products of relational systems and cardinal characteristics associated with Yorioka ideals.</div><div>In addition, we dissect and generalize results from Pawlikowski to force upper bounds of the covering of <span><math><mi>SN</mi></math></span>, particularly for finite support iterations of precaliber posets.</div><div>Finally, as applications of our main theorems, we prove consistency results about the cardinal characteristics associated with <span><math><mi>SN</mi></math></span> and the principle <span><math><mrow><mi>DS</mi></mrow><mo>(</mo><mi>δ</mi><mo>)</mo></math></span>. For example, we show that <span><math><mrow><mi>cov</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo><mo><</mo><mrow><mi>non</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo><mo>=</mo><mi>c</mi><mo><</mo><mrow><mi>cof</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo></math></span> holds in Cohen model, and we refine a result (and the proof) of the first author about the consistency of <span><math><mrow><mi>cov</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo><mo><</mo><mrow><mi>non</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo><mo><</mo><mrow><mi>cof</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo></math></span>, with <span><math><mi>c</mi></math></span> in any desired position with respect to <span><math><mrow><mi>cof</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo></math></span>, and the improvement that <span><math><mrow><mi>non</mi></mrow><mo>(</mo><mrow><mi>SN</mi></mrow><mo>)</mo></math></span> can be singular here.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 4","pages":"Article 103537"},"PeriodicalIF":0.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Positive definability patterns

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-28 DOI: 10.1016/j.apal.2024.103539

Ori Segel

We reformulate Hrushovski's definability patterns from the setting of first order logic to the setting of positive logic. Given an h-universal theory T we put two structures on the type spaces of models of T in two languages,

L

and

L_{π}

. It turns out that for sufficiently saturated models, the corresponding h-universal theories

T

and

T_{π}

are independent of the model. We show that there is a canonical model

J

T

, and in many interesting cases there is an analogous canonical model

J_{π}

T_{π}

, both of which embed into every type space. We discuss the properties of these canonical models, called cores, and give some concrete examples.

引用次数: 0

Strong standard completeness theorems for S5-modal Łukasiewicz logics 5-模态Łukasiewicz逻辑的强标准完备性定理

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-22 DOI: 10.1016/j.apal.2024.103529

Diego Castaño , José Patricio Díaz Varela , Gabriel Savoy

We study the S5-modal expansion of the Łukasiewicz logic. We exhibit a finitary propositional calculus and show that it is finitely strongly complete with respect to this logic. This propositional calculus is then expanded with an infinitary rule to achieve strong completeness. These results are derived from properties of monadic MV-algebras: functional representations of simple and finitely subdirectly irreducible algebras, as well as the finite embeddability property. We also show similar completeness theorems for the extension of the logic based on models with bounded universe.

我们研究了Łukasiewicz逻辑的s5模态展开。我们展示了一个有限命题演算，并证明了它对于这个逻辑是有限强完备的。然后用一个无限规则展开这个命题演算，以达到强完备性。这些结果来源于一元mv -代数的性质：简单和有限次直接不可约代数的泛函表示，以及有限可嵌入性。对于基于有界宇宙模型的逻辑扩展，我们也给出了类似的完备性定理。

引用次数: 0

Semiconic idempotent logic II: Beth definability and deductive interpolation

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-15 DOI: 10.1016/j.apal.2024.103528

Wesley Fussner , Nikolaos Galatos

Semiconic idempotent logic sCI is a common generalization of intuitionistic logic, semilinear idempotent logic sLI, and in particular relevance logic with mingle. We establish the projective Beth definability property and the deductive interpolation property for many extensions of sCI, and identify extensions where these properties fail. We achieve these results by studying the (strong) amalgamation property and the epimorphism-surjectivity property for the corresponding algebraic semantics, viz. semiconic idempotent residuated lattices. Our study is made possible by the structural decomposition of conic idempotent models achieved in the prequel, as well as a detailed analysis of the structure of idempotent residuated chains serving as index sets in this decomposition. Here we study the latter on two levels: as certain enriched Galois connections and as enhanced monoidal preorders. Using this, we show that although conic idempotent residuated lattices do not have the amalgamation property, the natural class of stratified and conjunctive conic idempotent residuated lattices has the strong amalgamation property, and thus has surjective epimorphisms. This extends to the variety generated by stratified and conjunctive conic idempotent residuated lattices, and we establish the (strong) amalgamation and epimorphism-surjectivity properties for several important subvarieties. Using the algebraizability of sCI, this yields the deductive interpolation property and the projective Beth definability property for the corresponding substructural logics extending sCI.

{"title":"Semiconic idempotent logic II: Beth definability and deductive interpolation","authors":"Wesley Fussner , Nikolaos Galatos","doi":"10.1016/j.apal.2024.103528","DOIUrl":"10.1016/j.apal.2024.103528","url":null,"abstract":"<div><div>Semiconic idempotent logic <strong>sCI</strong> is a common generalization of intuitionistic logic, semilinear idempotent logic <strong>sLI</strong>, and in particular relevance logic with mingle. We establish the projective Beth definability property and the deductive interpolation property for many extensions of <strong>sCI</strong>, and identify extensions where these properties fail. We achieve these results by studying the (strong) amalgamation property and the epimorphism-surjectivity property for the corresponding algebraic semantics, viz. semiconic idempotent residuated lattices. Our study is made possible by the structural decomposition of conic idempotent models achieved in the prequel, as well as a detailed analysis of the structure of idempotent residuated chains serving as index sets in this decomposition. Here we study the latter on two levels: as certain enriched Galois connections and as enhanced monoidal preorders. Using this, we show that although conic idempotent residuated lattices do not have the amalgamation property, the natural class of stratified and conjunctive conic idempotent residuated lattices has the strong amalgamation property, and thus has surjective epimorphisms. This extends to the variety generated by stratified and conjunctive conic idempotent residuated lattices, and we establish the (strong) amalgamation and epimorphism-surjectivity properties for several important subvarieties. Using the algebraizability of <strong>sCI</strong>, this yields the deductive interpolation property and the projective Beth definability property for the corresponding substructural logics extending <strong>sCI</strong>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 3","pages":"Article 103528"},"PeriodicalIF":0.6,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143148056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Failure of the Blok–Esakia Theorem in the monadic setting

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-11-14 DOI: 10.1016/j.apal.2024.103527

G. Bezhanishvili , L. Carai

The Blok–Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok–Esakia isomorphism σ does not extend to the fragments of the corresponding predicate logics of already one fixed variable. In other words, we prove that σ is no longer an isomorphism from the lattice of extensions of the monadic intuitionistic logic to the lattice of extensions of the monadic Grzegorczyk logic.

引用次数: 0

Universal proof theory: Feasible admissibility in intuitionistic modal logics 通用证明理论：直觉模态逻辑中的可行可接受性

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-10-23 DOI: 10.1016/j.apal.2024.103526

Amirhossein Akbar Tabatabai , Raheleh Jalali

We introduce a general and syntactically defined family of sequent-style calculi over the propositional language with the modalities

{□, ◇}

and its fragments as a formalization for constructively acceptable systems. Calling these calculi constructive, we show that any strong enough constructive sequent calculus, satisfying a mild technical condition, feasibly admits all Visser's rules. This means that there exists a polynomial-time algorithm that, given a proof of the premise of a Visser's rule, provides a proof for its conclusion. As a positive application, we establish the feasible admissibility of Visser's rules in sequent calculi for several intuitionistic modal logics, including

CK

IK

, their extensions by the modal axioms T, B, 4, 5, and the axioms for bounded width and depth and their fragments

{CK}_{□}

, propositional lax logic and

IPC

. On the negative side, we show that if a strong enough intuitionistic modal logic (satisfying a mild technical condition) does not admit at least one of Visser's rules, it cannot have a constructive sequent calculus. Consequently, no intermediate logic other than

IPC

has a constructive sequent calculus.

我们在模态为{□,◇}的命题语言及其片段上引入了一系列通用的、语法上定义的序列式计算，作为构造性可接受系统的形式化。我们称这些计算为构造式计算，并证明任何足够强的构造式顺序微积分，只要满足一个温和的技术条件，就可以接受所有的维塞尔规则。这意味着存在一种多项式时间算法，只要给定一个维塞尔规则的前提证明，就能为其结论提供证明。作为正面应用，我们为几种直觉模态逻辑建立了维塞尔规则在时序计算中的可行可接受性，这些模态逻辑包括 CK、IK 及其模态公理 T、B、4、5 的扩展，以及有界宽度和深度公理及其片段 CK□、命题宽松逻辑和 IPC。从反面来看，我们证明了如果一个足够强的直观模态逻辑（满足一个温和的技术条件）不接受至少一条维塞尔规则，它就不可能有构造时序微积分。因此，除了 IPC 之外，没有任何中间逻辑具有构造时序微积分。

{"title":"Universal proof theory: Feasible admissibility in intuitionistic modal logics","authors":"Amirhossein Akbar Tabatabai , Raheleh Jalali","doi":"10.1016/j.apal.2024.103526","DOIUrl":"10.1016/j.apal.2024.103526","url":null,"abstract":"<div><div>We introduce a general and syntactically defined family of sequent-style calculi over the propositional language with the modalities <span><math><mo>{</mo><mo>□</mo><mo>,</mo><mo>◇</mo><mo>}</mo></math></span> and its fragments as a formalization for constructively acceptable systems. Calling these calculi <em>constructive</em>, we show that any strong enough constructive sequent calculus, satisfying a mild technical condition, feasibly admits all Visser's rules. This means that there exists a polynomial-time algorithm that, given a proof of the premise of a Visser's rule, provides a proof for its conclusion. As a positive application, we establish the feasible admissibility of Visser's rules in sequent calculi for several intuitionistic modal logics, including <span><math><mi>CK</mi></math></span>, <span><math><mi>IK</mi></math></span>, their extensions by the modal axioms <em>T</em>, <em>B</em>, 4, 5, and the axioms for bounded width and depth and their fragments <span><math><msub><mrow><mi>CK</mi></mrow><mrow><mo>□</mo></mrow></msub></math></span>, propositional lax logic and <span><math><mi>IPC</mi></math></span>. On the negative side, we show that if a strong enough intuitionistic modal logic (satisfying a mild technical condition) does not admit at least one of Visser's rules, it cannot have a constructive sequent calculus. Consequently, no intermediate logic other than <span><math><mi>IPC</mi></math></span> has a constructive sequent calculus.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103526"},"PeriodicalIF":0.6,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bi-colored expansions of geometric theories 几何理论的双色展开

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2024-10-18 DOI: 10.1016/j.apal.2024.103525

S. Jalili , M. Pourmahdian , M. Khani

This paper concerns the study of expansions of models of a geometric theory T by a color predicate p, within the framework of the Fraïssé-Hrushovski construction method. For each

α \in (0, 1]

, we define a pre-dimension function

δ_{α}

on the class of Bi-colored models of

T^{\forall}

and consider the subclass

K_{α}^{+}

consisting of models with hereditary positive

δ_{α}

. We impose certain natural conditions on T that enable us to introduce a complete

Π_{2}

-theory

T_{α}

for the rich models in

K_{α}^{+}

. We show how the transfer of certain model-theoretic properties, such as NIP and strong-dependence, from T to

T_{α}

, depends on whether α is rational or irrational.

本文在弗拉伊塞-赫鲁晓夫斯基（Fraïssé-Hrushovski）构造方法的框架内，研究用颜色谓词 p 展开几何理论 T 的模型。对于每个 α∈(0,1]，我们在 T∀ 的双色模型类上定义一个前维度函数 δα，并考虑由具有遗传性正 δα 的模型组成的子类 Kα+。我们对 T 施加了某些自然条件，使我们能够为 Kα+ 中的丰富模型引入一个完整的 Π2 理论 Tα。我们展示了某些模型理论性质，如NIP和强依赖性，如何从T转移到Tα，取决于α是有理的还是无理的。

{"title":"Bi-colored expansions of geometric theories","authors":"S. Jalili , M. Pourmahdian , M. Khani","doi":"10.1016/j.apal.2024.103525","DOIUrl":"10.1016/j.apal.2024.103525","url":null,"abstract":"<div><div>This paper concerns the study of expansions of models of a geometric theory <em>T</em> by a color predicate <em>p</em>, within the framework of the Fraïssé-Hrushovski construction method. For each <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, we define a pre-dimension function <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> on the class of Bi-colored models of <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∀</mo></mrow></msup></math></span> and consider the subclass <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> consisting of models with hereditary positive <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>. We impose certain natural conditions on <em>T</em> that enable us to introduce a complete <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-theory <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> for the rich models in <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span>. We show how the transfer of certain model-theoretic properties, such as NIP and strong-dependence, from <em>T</em> to <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>, depends on whether <em>α</em> is rational or irrational.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103525"},"PeriodicalIF":0.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Annals of Pure and Applied Logic

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀