Archive for Mathematical Logic最新文献_第4页

On two consequences of CH established by Sierpiński 关于谢尔宾斯基确定的 CH 的两个后果

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-05-07 DOI: 10.1007/s00153-024-00925-6

R. Pol, P. Zakrzewski

引用次数: 0

Katětov order between Hindman, Ramsey and summable ideals Hindman 理想、Ramsey 理想和可求和理想之间的 Katětov 秩

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-05-03 DOI: 10.1007/s00153-024-00924-7

Rafał Filipów, Krzysztof Kowitz, Adam Kwela

{"title":"Katětov order between Hindman, Ramsey and summable ideals","authors":"Rafał Filipów, Krzysztof Kowitz, Adam Kwela","doi":"10.1007/s00153-024-00924-7","DOIUrl":"10.1007/s00153-024-00924-7","url":null,"abstract":"<div>A family (mathcal {I}) of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal (mathcal {I}) on X is below an ideal (mathcal {J}) on Y in the Katětov order if there is a function (f{: }Yrightarrow X) such that (f^{-1}[A]in mathcal {J}) for every (Ain mathcal {I}). We show that the Hindman ideal, the Ramsey ideal and the summable ideal are pairwise incomparable in the Katětov order, where<ul>\u0000 <li>\u0000 The Ramsey ideal consists of those sets of pairs of natural numbers which do not contain a set of all pairs of any infinite set (equivalently do not contain, in a sense, any infinite complete subgraph),\u0000 </li>\u0000 <li>\u0000 The Hindman ideal consists of those sets of natural numbers which do not contain any infinite set together with all finite sums of its members (equivalently do not contain IP-sets that are considered in Ergodic Ramsey theory),\u0000 </li>\u0000 <li>\u0000 The summable ideal consists of those sets of natural numbers such that the series of the reciprocals of its members is convergent.\u0000\u0000 </li>\u0000 </ul></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 7-8","pages":"859 - 876"},"PeriodicalIF":0.3,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00924-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885588","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

On undecidability of the propositional logic of an associative binary modality 论关联二元模态命题逻辑的不可判定性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-29 DOI: 10.1007/s00153-024-00921-w

Michael Kaminski

引用次数: 0

Quantifier-free induction for lists 列表的无量纲归纳法

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-20 DOI: 10.1007/s00153-024-00923-8

Stefan Hetzl, Jannik Vierling

引用次数: 0

Square compactness and Lindelöf trees 平方紧凑性和林德洛夫树

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-10 DOI: 10.1007/s00153-024-00918-5

Pedro E. Marun

引用次数: 0

The Josefson–Nissenzweig theorem and filters on (omega ) 约瑟夫森-尼森茨威格定理和 $$omega $$ 上的滤波器

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-09 DOI: 10.1007/s00153-024-00920-x

Witold Marciszewski, Damian Sobota

{"title":"The Josefson–Nissenzweig theorem and filters on (omega )","authors":"Witold Marciszewski, Damian Sobota","doi":"10.1007/s00153-024-00920-x","DOIUrl":"10.1007/s00153-024-00920-x","url":null,"abstract":"<div>For a free filter F on (omega ), endow the space (N_F=omega cup {p_F}), where (p_Fnot in omega ), with the topology in which every element of (omega ) is isolated whereas all open neighborhoods of (p_F) are of the form (Acup {p_F}) for (Ain F). Spaces of the form (N_F) constitute the class of the simplest non-discrete Tychonoff spaces. The aim of this paper is to study them in the context of the celebrated Josefson–Nissenzweig theorem from Banach space theory. We prove, e.g., that, for a filter F, the space (N_F) carries a sequence (langle mu _n:nin omega rangle ) of normalized finitely supported signed measures such that (mu _n(f)rightarrow 0) for every bounded continuous real-valued function f on (N_F) if and only if (F^*le _K{mathcal {Z}}), that is, the dual ideal (F^*) is Katětov below the asymptotic density ideal ({mathcal {Z}}). Consequently, we get that if (F^*le _K{mathcal {Z}}), then: (1) if X is a Tychonoff space and (N_F) is homeomorphic to a subspace of X, then the space (C_p^*(X)) of bounded continuous real-valued functions on X contains a complemented copy of the space (c_0) endowed with the pointwise topology, (2) if K is a compact Hausdorff space and (N_F) is homeomorphic to a subspace of K, then the Banach space C(K) of continuous real-valued functions on K is not a Grothendieck space. The latter result generalizes the well-known fact stating that if a compact Hausdorff space K contains a non-trivial convergent sequence, then the space C(K) is not Grothendieck.\u0000</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 7-8","pages":"773 - 812"},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00920-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583146","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

Games characterizing certain families of functions 表征某些函数族的博弈

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-06 DOI: 10.1007/s00153-024-00922-9

Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca

引用次数: 0

The extent of saturation of induced ideals 诱导理想的饱和程度

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-06 DOI: 10.1007/s00153-024-00919-4

Kenta Tsukuura

引用次数: 0

Herbrandized modified realizability 修正的可实现性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-04-04 DOI: 10.1007/s00153-024-00917-6

Gilda Ferreira, Paulo Firmino

引用次数: 0

Indiscernibles and satisfaction classes in arithmetic 算术中的不可分性和满足类

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-03-28 DOI: 10.1007/s00153-024-00915-8

Ali Enayat

{"title":"Indiscernibles and satisfaction classes in arithmetic","authors":"Ali Enayat","doi":"10.1007/s00153-024-00915-8","DOIUrl":"10.1007/s00153-024-00915-8","url":null,"abstract":"<div>We investigate the theory Peano Arithmetic with Indiscernibles ((textrm{PAI})). Models of (textrm{PAI}) are of the form (({mathcal {M}},I)), where ({mathcal {M}}) is a model of (textrm{PA}), I is an unbounded set of order indiscernibles over ({mathcal {M}}), and (({mathcal {M}},I)) satisfies the extended induction scheme for formulae mentioning I. Our main results are Theorems A and B following. Theorem A. Let ({mathcal {M}}) be a nonstandard model of (textrm{PA}) of any cardinality. (mathcal {M }) has an expansion to a model of (textrm{PAI}) iff ( {mathcal {M}}) has an inductive partial satisfaction class. Theorem A yields the following corollary, which provides a new characterization of countable recursively saturated models of (textrm{PA}): Corollary. A countable model ({mathcal {M}}) of (textrm{PA}) is recursively saturated iff ({mathcal {M}}) has an expansion to a model of (textrm{PAI}). Theorem B. There is a sentence (alpha ) in the language obtained by adding a unary predicate I(x) to the language of arithmetic such that given any nonstandard model ({mathcal {M}}) of (textrm{PA}) of any cardinality, ({mathcal {M}}) has an expansion to a model of (text {PAI}+alpha ) iff ({mathcal {M}}) has a inductive full satisfaction class.</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 5-6","pages":"655 - 677"},"PeriodicalIF":0.3,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00915-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314057","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