Annals of Pure and Applied Logic最新文献

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IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-05-05 DOI: 10.1016/j.apal.2025.103606

Vera Fischer , Sy David Friedman , David Schrittesser , Asger Törnquist

We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality

a_{g}

of a maximal cofinitary group (MCG) is strictly between

ℵ_{1}

and

c

, and there is a

Π_{2}^{1}

-definable MCG of this cardinality. Here

Π_{2}^{1}

is optimal, making this result a natural counterpart to the Borel MCG of Horowitz and Shelah. Our theorem has its analogue in the realm of maximal almost disjoint (MAD) families, extending a line of results regarding the definability properties of MAD families in models with large continuum.

本文提出了相邻自编码共限置换的一个新的强制概念，并利用它证明了最大共限群（MCG）的最小基数ag严格地存在于λ 1和λ c之间，并且存在这个基数的Π21-definable MCG。这里Π21是最优的，使这个结果与霍洛维茨和希拉的Borel MCG自然对应。我们的定理在极大几乎不相交族（MAD）领域有类似的结果，扩展了关于大连续统模型中极大几乎不相交族的可定义性的一系列结果。

引用次数: 0

Unreachability of Γ2n+1,m 无法到达Γ2n+1，m

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-04-23 DOI: 10.1016/j.apal.2025.103604

Derek Levinson

We find bounds for the maximal length of a sequence of distinct

Γ_{2n + 1, m}

-sets under AD and show there is no sequence of distinct

Γ_{2n + 1}

-sets of length

δ_{2n + 3}^{1}

. As a special case, there is no sequence of distinct

Γ_{1, m}

-sets of length

ℵ_{m + 2}

. These are the optimal results for the pointclasses

Γ_{2n + 1}

and

Γ_{1, m}

我们找到了在AD条件下具有不同Γ2n+1，m-集的序列的最大长度的界，并证明不存在具有不同Γ2n+1-集的序列，其长度为δ2n+31。作为一种特殊情况，不存在不同的序列Γ1，m-长度为λ m+2的集合。这些是pointclass Γ2n+1和Γ1，m的最佳结果。

引用次数: 0

Indestructible supercompactness and level by level inequivalence 不可摧毁的超紧性和逐级的不等价

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-05-30 DOI: 10.1016/j.apal.2025.103618

Arthur W. Apter

We construct via forcing a model for the level by level inequivalence between strong compactness and supercompactness containing a fully indestructible supercompact cardinal. This answers a question posed at the end of [2] and [6].

我们通过强迫构造了包含完全不可摧毁的超紧基数的强紧性和超紧性之间的逐级不等价模型。这回答了[2]和[6]结尾提出的一个问题。

引用次数: 0

Piecewise convex embeddability on linear orders 线性阶上的分段凸嵌入性

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-03-13 DOI: 10.1016/j.apal.2025.103581

Martina Iannella , Alberto Marcone , Luca Motto Ros , Vadim Weinstein

Given a nonempty set

L

of linear orders, we say that the linear order L is

L

-convex embeddable into the linear order

L^{'}

if it is possible to partition L into convex sets indexed by some element of

L

which are isomorphic to convex subsets of

L^{'}

ordered in the same way. This notion generalizes convex embeddability and (finite) piecewise convex embeddability (both studied in [13]), which are the special cases

L = {1}

and

L = Fin

. We focus mainly on the behavior of these relations on the set of countable linear orders, first characterizing when they are transitive, and hence a quasi-order. We then study these quasi-orders from a combinatorial point of view, and analyze their complexity with respect to Borel reducibility. Finally, we extend our analysis to uncountable linear orders.

给定一个线性阶的非空集合L，如果有可能将L划分为由L中的某些元素索引的凸集，且这些元素与L ‘的凸子集同构，则我们说线性阶L是L-凸可嵌入到线性阶L ’中的。这个概念推广了凸可嵌入性和（有限）分段凸可嵌入性（两者都在[13]中研究过），它们是L={1}和L=Fin的特殊情况。我们主要关注这些关系在可数线性阶集合上的行为，首先刻画了它们什么时候是可传递的，因此是一个拟阶。然后我们从组合的角度研究了这些拟序，并分析了它们在Borel可约性方面的复杂性。最后，我们将分析扩展到不可数线性阶。

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引用次数: 0

Generics in invariant subsets of the group of order preserving permutations of Q Q的保序置换群的不变子集中的泛型

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-03-25 DOI: 10.1016/j.apal.2025.103585

M. Drzewiecka , A. Ivanov , B. Mokry

Let

ρ \in Aut (Q, <)

and

C_{ρ}

be the closure of the conjugacy class of ρ in

Aut (Q, <)

. We show that

C_{ρ}

contains a conjugacy class, say C, which is comeagre in

C_{ρ}

. We describe representatives of C. Furthermore, we show that the family of finite partial maps extendable to elements of C has the cofinal amalgamation property.

设ρ∈Aut(Q,<)，且ρ是ρ在Aut（Q,<）中的共轭类的闭包。我们证明了C包含一个共轭类，比如C，它在C中是相合的。我们描述了C的代表，进一步证明了可扩展到C元素的有限部分映射族具有共终合并性质。

引用次数: 0

Descriptive complexity of topological invariants 拓扑不变量的描述复杂性

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-05-14 DOI: 10.1016/j.apal.2025.103611

Djamel Eddine Amir, Mathieu Hoyrup

In this article, we investigate the descriptive complexity of topological invariants. Our main goal is to understand the expressive power of low complexity invariants, by investigating which spaces they can distinguish. We study the invariants in the first two levels of the Borel hierarchy. We develop techniques to establish whether two spaces can be separated by invariants in these levels. We show that they are sufficient to separate finite topological graphs. We finally identify the complexity of recognizing the line segment.

在本文中，我们研究了拓扑不变量的描述复杂性。我们的主要目标是通过研究它们可以区分哪些空间来理解低复杂度不变量的表达能力。我们研究了Borel层次结构的前两层中的不变量。我们开发的技术，以确定是否两个空间可以由不变量在这些水平分开。证明了它们足以分离有限拓扑图。最后指出了线段识别的复杂性。

引用次数: 0

Interpolation in Hájek's basic logic 插值在Hájek的基本逻辑

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-05-26 DOI: 10.1016/j.apal.2025.103615

Wesley Fussner , Simon Santschi

We exhaustively classify varieties of BL-algebras with the amalgamation property, showing that there are only countably many of them and solving an open problem of Montagna. As a consequence of this classification, we obtain a complete description of which axiomatic extensions of Hájek's basic fuzzy logic BL have the deductive interpolation property. Along the way, we provide similar classifications of varieties of basic hoops with the amalgamation property and axiomatic extensions of the negation-free fragment of BL with the deductive interpolation property.

我们对具有合并性质的bl -代数进行了详尽的分类，证明了它们只有可数的几个，并解决了Montagna的一个开放问题。作为这种分类的结果，我们得到了Hájek的基本模糊逻辑BL的公理扩展具有演绎插值性质的完整描述。在此过程中，我们提供了具有合并性质的各种基本环的类似分类，以及具有演绎插值性质的BL无负片段的公理化扩展。

引用次数: 0

The Set-Cover game and non-measurable unions Set-Cover游戏和不可衡量的工会

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-04-07 DOI: 10.1016/j.apal.2025.103602

Taras Banakh , Robert Rałowski , Szymon Żeberski

Using a game-theoretic approach we present a generalization of the classical result of Brzuchowski, Cichoń, Grzegorek and Ryll-Nardzewski on non-measurable unions. We also present applications of obtained results to Marczewski–Burstin representable ideals.

本文利用博弈论的方法推广了Brzuchowski、cichoski、Grzegorek和Ryll-Nardzewski关于不可测并的经典结果。我们还介绍了所得结果在马尔切夫斯基-布尔斯汀可表征理想中的应用。

引用次数: 0

Some more results on relativized Chaitin's Ω 关于相对化柴廷的Ω的更多结果

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-04-04 DOI: 10.1016/j.apal.2025.103586

Liang Yu

We prove that, assuming ZF, and restricted to any

\leq_{T}

-pointed set, Chaitin's

Ω_{U} : x \mapsto Ω_{U}^{x} = \sum_{U^{x} (σ) ↓} 2^{- | σ |}

is not injective for any universal prefix-free Turing machine U, and that

Ω_{U}^{x}

fails to be degree invariant in a very strong sense, answering several recent questions in descriptive set theory. Moreover, we show that under

ZF + AD

, every function f mapping x to x-random must be uncountable-to-one over an upper cone of Turing degrees.

我们证明，假设 ZF，并限制于任何 ≤T 点集，柴廷的ΩU:x↦ΩUx=∑Ux(σ)↓2-|σ| 对于任何通用无前缀图灵机 U 都不是注入式的，并且ΩUx 在非常强的意义上不具有度不变性，这回答了描述集合论中最近的几个问题。此外，我们还证明了在 ZF+AD 下，映射 x 到 x-random 的每个函数 f 都必须在图灵度的上锥上是不可数到一的。

引用次数: 0

Equational definitions of logical filters 逻辑滤波器的等式定义

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic

Pub Date : 2025-08-01 Epub Date: 2025-05-28 DOI: 10.1016/j.apal.2025.103617

Michele Pra Baldi , Adam Přenosil

A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type of algebraic interpretation has been extensively studied and underlies the theory of algebraization, whereas little systematic attention has been paid to the latter type. We investigate a semantic form of the latter type of algebraic interpretation, which we call the equational definability of compact filters (EDCF). Paralleling the well-studied hierarchy of variants of the deduction–detachment theorem (DDT), this property also comes in local, parametrized, and parametrized local variants. The main results of this paper characterize of each of these variants of the EDCF in a spirit similar to the existing characterizations of the DDT. While the EDCF hierarchy and the DDT hierarchy coincide for algebraizable logics, part of the interest of the EDCF stems from the fact it is often enjoyed even by logics which are not well-behaved in terms of other existing classifications in algebraic logic.

有限命题逻辑可以用两种不同的方式进行代数解读：将公式转化为方程，将逻辑规则转化为准方程，或者将逻辑规则直接转化为方程。前一种类型的代数解释已经被广泛研究，是代数化理论的基础，而后一种类型的代数解释却很少得到系统的关注。我们研究了后一种代数解释的语义形式，我们称之为紧滤波器的等式可定义性（EDCF）。与演绎分离定理（DDT）的变体层次结构相似，这个性质也存在于局部、参数化和参数化的局部变体中。本文的主要结果以类似于DDT现有特征的精神描述了EDCF的每一个变体。虽然EDCF层次结构和DDT层次结构在可代数逻辑中是一致的，但EDCF的部分兴趣源于这样一个事实，即即使在代数逻辑中其他现有分类方面表现不好的逻辑也经常使用它。

引用次数: 0

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