Archive for Mathematical Logic最新文献_第7页

Filter pairs and natural extensions of logics 滤波器对与逻辑的自然扩展

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-07-02 DOI: 10.1007/s00153-022-00834-6

Peter Arndt, Hugo Luiz Mariano, Darllan Conceição Pinto

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引用次数: 1

Pseudointersection numbers, ideal slaloms, topological spaces, and cardinal inequalities 伪交数，理想回旋，拓扑空间，和基数不等式

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-07-01 DOI: 10.1007/s00153-022-00832-8

Jaroslav Šupina

{"title":"Pseudointersection numbers, ideal slaloms, topological spaces, and cardinal inequalities","authors":"Jaroslav Šupina","doi":"10.1007/s00153-022-00832-8","DOIUrl":"10.1007/s00153-022-00832-8","url":null,"abstract":"<div><p>We investigate several ideal versions of the pseudointersection number <span>(mathfrak {p})</span>, ideal slalom numbers, and associated topological spaces with the focus on selection principles. However, it turns out that well-known pseudointersection invariant <span>(mathtt {cov}^*({mathcal I}))</span> has a crucial influence on the studied notions. For an invariant <span>(mathfrak {p}_mathrm {K}({mathcal J}))</span> introduced by Borodulin-Nadzieja and Farkas (Arch. Math. Logic 51:187–202, 2012), and an invariant <span>(mathfrak {p}_mathrm {K}({mathcal I},{mathcal J}))</span> introduced by Repický (Real Anal. Exchange 46:367–394, 2021), we have </p><div><div><span>$$begin{aligned} min {mathfrak {p}_mathrm {K}({mathcal I}),mathtt {cov}^*({mathcal I})}=mathfrak {p},qquad min {mathfrak {p}_mathrm {K}({mathcal I},{mathcal J}),mathtt {cov}^*({mathcal J})}le mathtt {cov}^*({mathcal I}), end{aligned}$$</span></div></div><p>respectively. In addition to the first inequality, for a slalom invariant <span>(mathfrak {sl_e}({mathcal I},{mathcal J}))</span> introduced in Šupina (J. Math. Anal. Appl. 434:477–491, 2016), we show that </p><div><div><span>$$begin{aligned} min {mathfrak {p}_mathrm {K}({mathcal I}),mathfrak {sl_e}({mathcal I},{mathcal J}),mathtt {cov}^*({mathcal J})}=mathfrak {p}. end{aligned}$$</span></div></div><p>Finally, we obtain a consistency that ideal versions of the Fréchet–Urysohn property and the strictly Fréchet–Urysohn property are distinguished.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-022-00832-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42601506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2

An infinitary propositional probability logic 一个不定命题概率逻辑

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-06-25 DOI: 10.1007/s00153-022-00835-5

Stefano Baratella

引用次数: 0

Computable scott sentences for quasi–Hopfian finitely presented structures 拟Hopfian有限表示结构的可计算scott语句

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-06-25 DOI: 10.1007/s00153-022-00833-7

Gianluca Paolini

引用次数: 1

Second order arithmetic as the model companion of set theory 作为集合论模型伴侣的二阶算法

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-06-22 DOI: 10.1007/s00153-022-00831-9

Giorgio Venturi, Matteo Viale

{"title":"Second order arithmetic as the model companion of set theory","authors":"Giorgio Venturi, Matteo Viale","doi":"10.1007/s00153-022-00831-9","DOIUrl":"10.1007/s00153-022-00831-9","url":null,"abstract":"<div><p>This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework linking Woodin’s generic absoluteness results for second order number theory and the theory of universally Baire sets to model companionship and show that (with the required care in details) a <span>(Pi _2)</span>-property formalized in an appropriate language for second order number theory is forcible from some <span>(Tsupseteq mathsf {ZFC}+)</span><i>large cardinals</i> if and only if it is consistent with the universal fragment of <i>T</i> if and only if it is realized in the model companion of <i>T</i>. In particular we show that the first order theory of <span>(H_{omega _1})</span> is the model companion of the first order theory of the universe of sets assuming the existence of class many Woodin cardinals, and working in a signature with predicates for <span>(Delta _0)</span>-properties and for all universally Baire sets of reals. We will extend these results also to the theory of <span>(H_{aleph _2})</span> in a follow up of this paper.\u0000\u0000\u0000</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-022-00831-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43323002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3

The existence of states based on Glivenko semihoops 基于格列文科半篮的状态的存在性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-05-18 DOI: 10.1007/s00153-022-00830-w

Pengfei He, Juntao Wang, Jiang Yang

引用次数: 1

Implicit recursion-theoretic characterizations of counting classes 计数类的隐式递归理论特征

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-05-03 DOI: 10.1007/s00153-022-00828-4

Ugo Dal Lago, Reinhard Kahle, Isabel Oitavem

引用次数: 1

(Delta ^0_1) variants of the law of excluded middle and related principles (Delta ^0_1) 排除中间和相关原则的法律变体

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-04-29 DOI: 10.1007/s00153-022-00827-5

Makoto Fujiwara

引用次数: 0

Type space functors and interpretations in positive logic 正逻辑中的类型空间函子及其解释

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-03-30 DOI: 10.1007/s00153-022-00825-7

Mark Kamsma

引用次数: 6

Destructibility and axiomatizability of Kaufmann models 考夫曼模型的可破坏性和公理化性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-03-26 DOI: 10.1007/s00153-022-00826-6

Corey Bacal Switzer

{"title":"Destructibility and axiomatizability of Kaufmann models","authors":"Corey Bacal Switzer","doi":"10.1007/s00153-022-00826-6","DOIUrl":"10.1007/s00153-022-00826-6","url":null,"abstract":"<div><p>A Kaufmann model is an <span>(omega _1)</span>-like, recursively saturated, rather classless model of <span>({{mathsf {P}}}{{mathsf {A}}})</span> (or <span>({{mathsf {Z}}}{{mathsf {F}}} )</span>). Such models were constructed by Kaufmann under the combinatorial principle <span>(diamondsuit _{omega _1})</span> and Shelah showed they exist in <span>(mathsf {ZFC})</span> by an absoluteness argument. Kaufmann models are an important witness to the incompactness of <span>(omega _1)</span> similar to Aronszajn trees. In this paper we look at some set theoretic issues related to this motivated by the seemingly naïve question of whether such a model can be “killed” by forcing without collapsing <span>(omega _1)</span>. We show that the answer to this question is independent of <span>(mathsf {ZFC})</span> and closely related to similar questions about Aronszajn trees. As an application of these methods we also show that it is independent of <span>(mathsf {ZFC})</span> whether or not Kaufmann models can be axiomatized in the logic <span>(L_{omega _1, omega } (Q))</span> where <i>Q</i> is the quantifier “there exists uncountably many”.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-022-00826-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33515747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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