Annals of Pure and Applied Logic最新文献

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Halfway new cardinal characteristics 半新基本特征

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103303

Jörg Brendle , Lorenz J. Halbeisen , Lukas Daniel Klausner , Marc Lischka , Saharon Shelah

Based on the well-known cardinal characteristics $s$ , $r$ and $i$ , we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e.g. the consistency of $s < s_{\frac{1}{2}}$ , as well as several results about possible values of $i_{\frac{1}{2}}$ .

在已知的基数特征s、r和i的基础上，我们引入了九个相关的基数特征，利用渐近密度的概念来刻画无穷集的不同相交性质。我们证明了几个界和一致性结果，例如s<；s12，以及关于i12的可能值的几个结果。

引用次数: 3

Computable Stone spaces 可计算石空间

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103304

Nikolay Bazhenov , Matthew Harrison-Trainor , Alexander Melnikov

We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper we focus on Stone spaces. We use Stone duality to construct the first known example of a computable topological Polish space not homeomorphic to any computably metrized space. In fact, in our proof we construct a right-c.e. metrized Stone space which is not homeomorphic to any computably metrized space. Then we introduce a new notion of effective categoricity for effectively compact spaces and prove that effectively categorical Stone spaces are exactly the duals of computably categorical Boolean algebras. Finally, we prove that, for a Stone space X, the Banach space $C (X; R)$ has a computable presentation if, and only if, X is homeomorphic to a computably metrized space. This gives an unexpected positive partial answer to a question recently posed by McNicholl.

我们研究了波兰空间到同胚的可计算度量性。在这篇论文中，我们关注的是石头空间。我们使用Stone对偶来构造第一个已知的可计算拓扑波兰空间的例子，该空间不同胚于任何可计算度量空间。事实上，在我们的证明中，我们构造了一个右c度量的Stone空间，它与任何可计算度量的空间都不是同胚的。然后，我们引入了有效紧致空间的有效范畴性的新概念，并证明了有效范畴Stone空间正是可计算范畴布尔代数的对偶。最后，我们证明了，对于Stone空间X，Banach空间C（X；R）具有可计算表示，当且仅当X同胚于可计算度量空间。这给了McNicholl最近提出的一个问题一个出乎意料的积极的部分答案。

引用次数: 6

Fresh function spectra 新函数谱

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-10-01 DOI: 10.1016/j.apal.2023.103300

Vera Fischer, Marlene Koelbing, Wolfgang Wohofsky

In this paper, we investigate the fresh function spectrum of forcing notions, where a new function on an ordinal is called fresh if all its initial segments are in the ground model. We determine the fresh function spectrum of several forcing notions and discuss the difference between fresh functions and fresh subsets. Furthermore, we consider the question which sets are realizable as the fresh function spectrum of a homogeneous forcing. We show that under GCH all sets with a certain closure property are realizable, while consistently there are sets which are not realizable.

在本文中，我们研究了强迫概念的新函数谱，其中如果序数上的新函数的所有初始段都在地面模型中，则称其为新函数。我们确定了几个强迫概念的新函数谱，并讨论了新函数和新子集之间的区别。此外，我们还考虑了哪些集合可以实现为齐次强迫的新函数谱的问题。我们证明了在GCH下，所有具有一定闭包性质的集合都是可实现的，而一致存在不可实现的集合。

引用次数: 0

Towards a finer classification of strongly minimal sets 论强极小集的更精细分类

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-28 DOI: 10.1016/j.apal.2023.103376

John T. Baldwin , Viktor V. Verbovskiy

Let M be strongly minimal and constructed by a ‘Hrushovski construction’ with a single ternary relation. If the Hrushovski algebraization function μ is in a certain class $T$ (μ triples) we show that for independent I with $| I | > 1$ , ${dcl}^{⁎} (I) = \emptyset$ (* means not in dcl of a proper subset). This implies the only definable truly n-ary functions f (f ‘depends’ on each argument), occur when $n = 1$ . We prove for Hrushovski's original construction and for the strongly minimal k-Steiner systems of Baldwin and Paolini that the symmetric definable closure, ${sdcl}^{⁎} (I) = \emptyset$ (Definition 2.7). Thus, no such theory admits elimination of imaginaries. As, we show that in an arbitrary strongly minimal theory, elimination of imaginaries implies ${sdcl}^{⁎} (I) \neq \emptyset$ . In particular, such strongly minimal Steiner systems with line-length at least 4 do not interpret a quasigroup, even though they admit a coordinatization if $k = p^{n}$ . The case structure depends on properties of the Hrushovski μ-function. The proofs depend on our introduction, for appropriate $G \subseteq aut (M)$ (setwise or pointwise stabilizers of finite independent sets), the notion of a G-normal substructure $A$ of M and of a G-decomposition of any finite such $A$ . These results lead to a finer classification of strongly minimal structures with flat geometry, according to what sorts of definable functions they admit.

设M是强极小的，并由具有单个三元关系的“Hrushovski构造”构造。如果Hrushovski代数函数μ在某一类T（μ三元组）中，我们证明了对于|I|>；1，dcl？（I）=∅（*表示不在适当子集的dcl中）。这意味着当n=1时，只有可定义的真正n元函数f（f“取决于”每个参数）才会出现。我们证明了Hrushovski的原始构造和Baldwin和Paolini的强极小k-Steiner系统的对称可定义闭包sdcl（I）=∅（定义2.7）。因此，没有这样的理论允许消除想象。正如，我们证明了在任意强极小理论中，想象的消去意味着sdcl≠（I）≠∅。特别地，这样的线长度至少为4的强极小Steiner系统不能解释拟群，即使它们在k=pn的情况下允许配位。格结构取决于Hrushovskiμ-函数的性质。证明取决于我们对适当的G⊆aut（M）（有限独立集的集向或点向稳定器）、M的G-正规子结构a和任何有限这样的a的G-分解的概念的引入。这些结果导致了具有平面几何的强极小结构的更细分类，根据它们允许的可定义函数的种类。

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引用次数: 2

Classification of ℵ0-categorical C-minimal pure C-sets c -极小纯c集的分类

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-27 DOI: 10.1016/j.apal.2023.103375

Françoise Delon , Marie-Hélène Mourgues

We classify all $ℵ_{0}$ -categorical and C-minimal C-sets up to elementary equivalence. As usual the Ryll-Nardzewski Theorem makes the classification of indiscernible $ℵ_{0}$ -categorical C-minimal sets as a first step. We first define solvable good trees, via a finite induction. The trees involved in initial and induction steps have a set of nodes, either consisting of a singleton, or having dense branches without endpoints and the same number of branches at each node. The class of colored good trees is the elementary class of solvable good trees. We show that a pure C-set M is indiscernible, finite or $ℵ_{0}$ -categorical and C-minimal iff its canonical tree $T (M)$ is a colored good tree. The classification of general $ℵ_{0}$ -categorical and C-minimal C-sets is done via finite trees with labeled vertices and edges, where labels are natural numbers, or infinity and complete theories of indiscernible, $ℵ_{0}$ -categorical or finite, and C-minimal C-sets.

我们对所有ℵ0-范畴和C-极小C-集直至初等等价。像往常一样，Ryll-Nardzewski定理使得不可分辨的分类ℵ0-范畴C-极小集作为第一步。我们首先通过有限归纳定义了可解的好树。初始步骤和归纳步骤中涉及的树有一组节点，要么由单个节点组成，要么具有没有端点的密集分支，每个节点的分支数量相同。有色好树类是可解好树的初等类。我们证明了纯C集M是不可分辨的、有限的或ℵ0-范畴和C-极小当其正则树T（M）是有色好树。一般的分类ℵ0-范畴和C-极小C-集是通过具有标记顶点和边的有限树来实现的，其中标记是自然数，或无穷大和不可分辨的完全理论，ℵ0-范畴或有限的C-极小C-集。

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引用次数: 0

Positive modal logic beyond distributivity 超越分布性的正模态逻辑

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-26 DOI: 10.1016/j.apal.2023.103374

Nick Bezhanishvili , Anna Dmitrieva , Jim de Groot , Tommaso Moraschini

We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of $Π_{1}$ -persistence and show that every weak positive modal logic is $Π_{1}$ -persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist's correspondence result.¹

我们为不需要分配的（模态）格发展了对偶性，并用它来研究超越分配性的正（模态）逻辑，我们称之为弱正（模式）逻辑。这种对偶建立在满足半格的Hofmann、Mislove和Stralka对偶的基础上。我们引入了π1-持久性的概念，并证明了每一个弱正模态逻辑都是π1-持久的。这种方法为弱正模态逻辑带来了一种新的关系语义，我们证明了其类似于Sahlqvist的对应结果。1

引用次数: 4

Weak saturation properties and side conditions 弱饱和特性和侧面条件

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-06 DOI: 10.1016/j.apal.2023.103356

Monroe Eskew

Towards combining “compactness” and “hugeness” properties at $ω_{2}$ , we investigate the relevance of side-conditions forcing. We reduce the upper bound on the consistency strength of the weak Chang's Conjecture at $ω_{2}$ using Neeman's forcing. On the other hand, we find a barrier to the applicability of these methods to our problem and give a counterexample to a claim of Neeman about the effects of iterating such forcing.

为了结合ω2的“紧性”和“巨大性”性质，我们研究了侧条件强迫的相关性。我们利用尼曼力降低了弱张氏猜想在ω2处的一致性强度的上界。另一方面，我们发现了将这些方法应用于我们的问题的一个障碍，并给出了尼曼关于迭代这种强迫的影响的主张的反例。

引用次数: 0

Absoluteness for the theory of the inner model constructed from finitely many cofinality quantifiers 由有限多个共定性量词构造的内部模型理论的绝对性

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-01 DOI: 10.1016/j.apal.2023.103358

Ur Ya'ar

We prove that the theory of the models constructible using finitely many cofinality quantifiers – $C_{λ_{1}, \dots, λ_{n}}^{⁎}$ and $C_{< λ_{1}, \dots, < λ_{n}}^{⁎}$ for $λ_{1}, \dots, λ_{n}$ regular cardinals – is set-forcing absolute under the assumption of class many Woodin cardinals, and is independent of the regular cardinals used. Towards this goal we prove some properties of the generic embedding induced from the stationary tower restricted to <μ-closed sets.

证明了λ1，…，λn和λ1，…，λn对λ1，…，λn的有限多个共度量词模型的理论在类多Woodin基数的假设下是集强迫绝对的，并且与所使用的正则基数无关。为此，我们证明了由μ闭集约束的固定塔导出的一般嵌入的一些性质。

引用次数: 0

Generalized fusible numbers and their ordinals 广义可熔数及其序数

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-01 DOI: 10.1016/j.apal.2023.103355

Alexander I. Bufetov , Gabriel Nivasch , Fedor Pakhomov

<div>Erickson defined the fusible numbers as a set <math><mi>F</mi></math> of reals generated by repeated application of the function <math><mfrac><mrow><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>. Erickson, Nivasch, and Xu showed that <math><mi>F</mi></math> is well ordered, with order type <math><msub><mrow><mi>ε</mi></mrow><mrow><mn>0</mn></mrow></msub></math>. They also investigated a recursively defined function <math><mi>M</mi><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></math>. They showed that the set of points of discontinuity of M is a subset of <math><mi>F</mi></math> of order type <math><msub><mrow><mi>ε</mi></mrow><mrow><mn>0</mn></mrow></msub></math>. They also showed that, although M is a total function on <math><mi>R</mi></math>, the fact that the restriction of M to <math><mi>Q</mi></math> is total is not provable in first-order Peano arithmetic <math><mi>PA</mi></math>.In this paper we explore the problem (raised by Friedman) of whether similar approaches can yield well-ordered sets <math><mi>F</mi></math> of larger order types. As Friedman pointed out, Kruskal's tree theorem yields an upper bound of the small Veblen ordinal for the order type of any set generated in a similar way by repeated application of a monotone function <math><mi>g</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><mi>R</mi></math>.The most straightforward generalization of <math><mfrac><mrow><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> to an n-ary function is the function <math><mfrac><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></math>. We show that this function generates a set <math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></math> whose order type is just <math><msub><mrow><mi>φ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo></math>. For this, we develop recursively defined functions <math><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></math> naturally generalizing the function M.Furthermore, we prove that for any linear function <math><mi>g</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><mi>R</mi></math>, the order type of the resulting <math><mi>F</mi></math> is at most <math><msub><mrow><mi>φ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mn>0</mn><

Erickson将可熔数定义为通过重复应用函数x+y+12生成的实数集F。Erickson、Nivasch和Xu证明了F是有序的，其有序类型为ε0。他们还研究了一个递归定义的函数M:R→R。他们证明了M的不连续点集是阶型ε0的F的子集。他们还证明，尽管M是R上的一个全函数，但在一阶Peano算术PA中，M对Q的限制是全的这一事实是不可证明的。在本文中，我们探讨了类似方法是否可以产生更高阶类型的良序集F的问题（由Friedman提出）。正如Friedman所指出的，Kruskal树定理为通过重复应用单调函数g:Rn以类似方式生成的任何集合的阶类型产生了小Veblen序数的上界→R.x+y+12对n元函数最直接的推广是函数x1+…+xn+1n。我们证明了这个函数生成了一个集合Fn，它的阶型恰好是φn-1（0）。为此，我们开发了递归定义的函数Mn:R→R自然地推广了函数M。此外，我们证明了对于任何线性函数g:Rn→R、得到的F的阶型至多为φn−1（0）。最后，我们证明了确实存在连续函数g:Rn→R，其结果集F的阶类型接近小的Veblen序数。

引用次数: 0

Extensions of Solovay's system S without independent sets of axioms 没有独立公理集的Solovay系统s的扩张

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2023-09-01 DOI: 10.1016/j.apal.2023.103360

Igor Gorbunov , Dmitry Shkatov

Chagrov and Zakharyaschev posed the problem of existence of extensions of Solovay's system S, which is a non-normalizable quasi-normal modal logic, that do not admit deductively independent sets of axioms. This paper gives a solution by exhibiting countably many extensions of S without deductively independent sets of axioms.

Chagrov和Zakharyaschev提出了Solovay系统S的扩展的存在性问题，Solovay系统S是一个不可归一化的拟正态模态逻辑，它不允许演绎独立的公理集。本文给出了一个解，给出了无演绎独立公理集的S的可数扩展。

引用次数: 0

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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.

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