该杂志发表研究论文，偶尔也会发表关于数理逻辑的调查或阐述。只要数理逻辑的方法发挥重要作用，也欢迎其他相关领域的贡献，例如理论计算机科学或哲学。因此，该杂志面向对数理逻辑在各自领域的应用及其与其他研究领域的互动感兴趣的逻辑学家和数学家、计算机科学家和哲学家。

The Archive for Mathematical Logic is a journal dedicated to research in mathematical logic, primarily publishing research papers and occasionally featuring surveys or expository articles on the subject. The journal welcomes contributions from other related fields, particularly theoretical computer science and philosophy, as long as they significantly utilize methods from mathematical logic. Thus, it targets logicians, mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their respective fields and its interactions with other areas of research.

《Archive for Mathematical Logic》是一本专注于数理逻辑研究的期刊，主要发表研究论文，偶尔也会刊登关于数理逻辑的综述或阐述性文章。该期刊欢迎任何在数理逻辑方法上具有重要贡献的相关领域的研究，尤其是理论计算机科学和哲学。因此，它的目标读者包括对数理逻辑在各自领域的应用及其与其他研究领域的互动感兴趣的逻辑学家、数学家、计算机科学家和哲学家。

Archive for Mathematical Logic

Hyoyoon Lee

Junguk Lee

Relativized Galois groups of first order theories over a hyperimaginary

超虚数域上的一阶理论的相对化伽罗瓦群

Abstract We investigate whether classical combinatorial theorems are provable in ZF. Some statements are not provable in ZF, but they are equivalent within ZF. For example, the following statements (i)–(iii) are equivalent: $$cf({\omega }_1)={\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> , $${\omega }_1\rightarrow ({\omega }_1,{\omega }+1)^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>→</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , any family $$\mathcal {A}\subset [{On}]^{&lt;{\omega }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:mrow> <mml:mi>On</mml:mi> </mml:mrow> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> of size $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> contains a $$\Delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -system of size $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> . Some classical results cannot be proven in ZF alone; however, we can establish weaker versions of these statements within the framework of ZF, such as $${{\omega }_2}\rightarrow ({\omega }_1,{\omega }+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>→</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , any family $$\mathcal {A}\subset [{On}]^{&lt;{\omega }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:mrow> <mml:mi>On</mml:mi> </mml:mrow> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> of size $${\omega }_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> contains a $$\Delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -system of size $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> . Some statements can be proven in ZF using purely combinatorial arguments, such as: given a set mapping $$F:{\omega }_1\rightarrow {[{\omega }_1]}^{&lt;{\omega }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>→</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , the set $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> has a partition into $${\omega }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> -many F -free sets. Other statements can be proven in ZF by employing certain methods of absoluteness, for example: given a set mapping $$F:{\omega }_1\rightarrow {[{\omega }_1]}^{&lt;{\omega }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>→</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , there is an F -free set of size $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> , for each $$n\in {\omega }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> , every family $$\mathcal {A}\subset {[{\omega }_1]}^{{\omega }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mi>ω</mml:mi> </mml:msup> </mml:mrow> </mml:math> with $$|A\cap B|\le n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>A</mml:mi> <mml:mo>∩</mml:mo> <mml:mi>B</mml:mi> <mml:mo>|</mml:mo> <mml:mo>≤</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> for $$\{A,B\}\in {[\mathcal {A}]}^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>A</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> has property B . In contrast to statement (5), we show that the following ZFC theorem of Komjáth is not provable from ZF + $$cf({\omega }_1)={\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> : (6 $$ ^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mmultiscripts> </mml:math> ) every family $$\mathcal {A}\subset {[{\omega }_1]}^{{\omega }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mi>ω</mml:mi> </mml:msup> </mml:mrow> </mml:math> with $$|A\cap B|\le 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>A</mml:mi> <mml:mo>∩</mml:mo> <mml:mi>B</mml:mi> <mml:mo>|</mml:mo> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> for $$\{A,B\}\in {[\mathcal {A}]}^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>A</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> is essentially disjoint . A function f is a uniform denumeration on $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> iff $${\text {dom}}(f)={\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>dom</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> , and for every $$1\le {\alpha }&lt;{\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>α</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> , $$f({\alpha })$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is a function from $${\omega }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> onto $${\alpha }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> . It is easy to see that the existence of a uniform denumeration of $${\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> implies $$cf({\omega }_1)={\omega }_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> . We prove that the failure of the reverse implication is equiconsistent with the existence of an inaccessible cardinal.

Tamás Csernák

Lajos Soukup

Infinite combinatorics revisited in the absence of Axiom of choice

无限组合数学在选择公理缺失情况下的再探讨

Abstract We investigate the degree spectra of computable relations on canonically ordered natural numbers $$(\omega ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and integers $$(\zeta ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . As for $$(\omega ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , we provide several criteria that fix the degree spectrum of a computable relation to all c.e. or to all $$\Delta _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Δ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> degrees; this includes the complete characterization of the degree spectra of so-called computable block functions that have only finitely many types of blocks. Compared to Bazhenov et al. (in: LIPIcs, vol 219, pp 8:1–8:20, 2022), we obtain a more general solution to the problem regarding possible degree spectra on $$(\omega ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , answering the question whether there are infinitely many such spectra. As for $$(\zeta ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , we prove the following dichotomy result: given an arbitrary computable relation R on $$(\zeta ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , its degree spectrum is either trivial or it contains all c.e. degrees. This result, and the proof techniques required to solve it, extend the analogous theorem for $$(\omega ,&lt;)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> obtained by Wright (Computability 7:349–365, 2018), and provide initial insight to Wright’s question whether such a dichotomy holds on computable ill-founded linear orders. This article is an extended version of Bazhenov et al. (in: LIPIcs, vol 219, pp 8:1–8:20, 2022).

Nikolay Bazhenov

Dariusz Kalociński

Michał Wrocławski

Degrees of relations on canonically ordered natural numbers and integers

规范有序的自然数和整数上的关系度

Ziemowit Kostana

What would the rational Urysohn space and the random graph look like if they were uncountable?

如果乌雷松空间和随机图是无穷的，它们会是什么样子？

Abstract We consider a question of Pereira as to whether the characteristic function of an internally approachable model can lead to free subsets for functions of the model. Pereira isolated the pertinent Approachable Free Subsets Property (AFSP) in his work on the $${\text {pcf}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>pcf</mml:mtext> </mml:math> -conjecture. A recent related property is the Approachable Bounded Subset Property (ABSP) of Ben-Neria and Adolf, and we here directly show it requires modest large cardinals to establish: Theorem If ABSP holds for an ascending sequence $$ \langle \aleph _{n_{m}} \rangle _{m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>m</mml:mi> </mml:msub> </mml:math> $$( n_{m} \in \omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> then there is an inner model with measurables $$\kappa &lt; \aleph _{\omega }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>κ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mi>ω</mml:mi> </mml:msub> </mml:mrow> </mml:math> of arbitrarily large Mitchell order below $$\aleph _{\omega }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mi>ω</mml:mi> </mml:msub> </mml:math> , that is: $$\sup \left\{ \alpha \mid {\exists }\kappa &lt; \aleph _{\omega } o ( \kappa ) \ge \alpha \right\} = \aleph _{\omega }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>sup</mml:mo> <mml:mfenced> <mml:mi>α</mml:mi> <mml:mo>∣</mml:mo> <mml:mo>∃</mml:mo> <mml:mi>κ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mi>ω</mml:mi> </mml:msub> <mml:mi>o</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>κ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≥</mml:mo> <mml:mi>α</mml:mi> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mi>ω</mml:mi> </mml:msub> </mml:mrow> </mml:math> . A result of Adolf and Ben Neria then shows that this conclusion is in fact the exact consistency strength of ABSP for such an ascending sequence. Their result went via the consistency of the non-existence of continuous tree-like scales; the result of this paper is direct and avoids the use of PCF scales.

短名	Arch. Math. Logic
Journal Impact	0.45
国际分区	MATHEMATICS(Q4)
期刊索引	SCI Q4中科院 4 区

ISSN	0933-5846, 1432-0665
h-index	32
国内分区	数学(4区)数学逻辑学(4区)数学数学(4区)

涉及主题	数学纯数学离散数学域代数上的计算机科学组合数学哲学程序设计语言数学分析物理语言学几何学人工智能认识论
出版信息	出版商: Springer New York，出版周期: 8 issues per year，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 1988，原创研究文献占比: 100.00%，自引率:0.00%， Gold OA占比: 32.39%

Archive for Mathematical Logic

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Relativized Galois groups of first order theories over a hyperimaginary

Infinite combinatorics revisited in the absence of Axiom of choice

Degrees of relations on canonically ordered natural numbers and integers

What would the rational Urysohn space and the random graph look like if they were uncountable?

Free subsets in internally approachable models

Relativized Galois groups of first order theories over a hyperimaginary

Infinite combinatorics revisited in the absence of Axiom of choice

What would the rational Urysohn space and the random graph look like if they were uncountable?

Degrees of relations on canonically ordered natural numbers and integers

Free subsets in internally approachable models