发布求助
文献互助 智能选刊 最新文献

Archive for Mathematical Logic最新文献

筛选
英文 中文
Positive indiscernibles 积极的不可辨认性
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-05-10 DOI: 10.1007/s00153-024-00928-3
Mark Kamsma
{"title":"Positive indiscernibles","authors":"Mark Kamsma","doi":"10.1007/s00153-024-00928-3","DOIUrl":"https://doi.org/10.1007/s00153-024-00928-3","url":null,"abstract":"<p>We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str<span>(_0)</span>-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing—rather than locally basing or EM-basing—str-trees on s-trees and str<span>(_0)</span>-trees on str-trees. As an application we show that a thick positive theory has <i>k</i>-<span>(mathsf {TP_2})</span> iff it has 2-<span>(mathsf {TP_2})</span></p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral MV-algebras and equispectrality 频谱 MV 算法和等谱性
IF 0.3 4区 数学
Archive for Mathematical Logic Pub Date : 2024-05-08 DOI: 10.1007/s00153-024-00926-5
Giuseppina Gerarda Barbieri, Antonio Di Nola, Giacomo Lenzi
{"title":"Spectral MV-algebras and equispectrality","authors":"Giuseppina Gerarda Barbieri, Antonio Di Nola, Giacomo Lenzi","doi":"10.1007/s00153-024-00926-5","DOIUrl":"https://doi.org/10.1007/s00153-024-00926-5","url":null,"abstract":"<p>In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes’ property. We show that an MV-algebra admits a state with the Bayes’ property if and only if it is bipartite.</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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
{"title":"On two consequences of CH established by Sierpiński","authors":"R. Pol, P. Zakrzewski","doi":"10.1007/s00153-024-00925-6","DOIUrl":"https://doi.org/10.1007/s00153-024-00925-6","url":null,"abstract":"<p>We study the relations between two consequences of the Continuum Hypothesis discovered by Wacław Sierpiński, concerning uniform continuity of continuous functions and uniform convergence of sequences of real-valued functions, defined on subsets of the real line of cardinality continuum.</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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":"https://doi.org/10.1007/s00153-024-00924-7","url":null,"abstract":"<p>A family <span>(mathcal {I})</span> of subsets of a set <i>X</i> is an <i>ideal on X</i> if it is closed under taking subsets and finite unions of its elements. An ideal <span>(mathcal {I})</span> on <i>X</i> is below an ideal <span>(mathcal {J})</span> on <i>Y</i> in the <i>Katětov order</i> if there is a function <span>(f{: }Yrightarrow X)</span> such that <span>(f^{-1}[A]in mathcal {J})</span> for every <span>(Ain mathcal {I})</span>. We show that the Hindman ideal, the Ramsey ideal and the summable ideal are pairwise incomparable in the Katětov order, where</p><ul>\u0000<li>\u0000<p>The <i>Ramsey ideal</i> 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),</p>\u0000</li>\u0000<li>\u0000<p>The <i>Hindman ideal</i> 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),</p>\u0000</li>\u0000<li>\u0000<p>The <i>summable ideal</i> consists of those sets of natural numbers such that the series of the reciprocals of its members is convergent.\u0000</p>\u0000</li>\u0000</ul>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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
{"title":"On undecidability of the propositional logic of an associative binary modality","authors":"Michael Kaminski","doi":"10.1007/s00153-024-00921-w","DOIUrl":"https://doi.org/10.1007/s00153-024-00921-w","url":null,"abstract":"<p>It is shown that both classical and intuitionistic propositional logics of an associative binary modality are undecidable. The proof is based on the deduction theorem for these logics.</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
{"title":"Quantifier-free induction for lists","authors":"Stefan Hetzl, Jannik Vierling","doi":"10.1007/s00153-024-00923-8","DOIUrl":"https://doi.org/10.1007/s00153-024-00923-8","url":null,"abstract":"<p>We investigate quantifier-free induction for Lisp-like lists constructed inductively from the empty list <span>( nil )</span> and the operation <span>({textit{cons}})</span>, that adds an element to the front of a list. First we show that, for <span>(m ge 1)</span>, quantifier-free <span>(m)</span>-step induction does not simulate quantifier-free <span>((m + 1))</span>-step induction. Secondly, we show that for all <span>(m ge 1)</span>, quantifier-free <span>(m)</span>-step induction does not prove the right cancellation property of the concatenation operation on lists defined by left-recursion.\u0000</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140624920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
{"title":"Square compactness and Lindelöf trees","authors":"Pedro E. Marun","doi":"10.1007/s00153-024-00918-5","DOIUrl":"https://doi.org/10.1007/s00153-024-00918-5","url":null,"abstract":"<p>We prove that every weakly square compact cardinal is a strong limit cardinal, and therefore weakly compact. We also study Aronszajn trees with no uncountable finitely splitting subtrees, characterizing them in terms of being Lindelöf with respect to a particular topology. We prove that the class of such trees is consistently non-empty and lies between the classes of Suslin and Aronszajn trees.</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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":"https://doi.org/10.1007/s00153-024-00920-x","url":null,"abstract":"<p>For a free filter <i>F</i> on <span>(omega )</span>, endow the space <span>(N_F=omega cup {p_F})</span>, where <span>(p_Fnot in omega )</span>, with the topology in which every element of <span>(omega )</span> is isolated whereas all open neighborhoods of <span>(p_F)</span> are of the form <span>(Acup {p_F})</span> for <span>(Ain F)</span>. Spaces of the form <span>(N_F)</span> 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 <i>F</i>, the space <span>(N_F)</span> carries a sequence <span>(langle mu _n:nin omega rangle )</span> of normalized finitely supported signed measures such that <span>(mu _n(f)rightarrow 0)</span> for every bounded continuous real-valued function <i>f</i> on <span>(N_F)</span> if and only if <span>(F^*le _K{mathcal {Z}})</span>, that is, the dual ideal <span>(F^*)</span> is Katětov below the asymptotic density ideal <span>({mathcal {Z}})</span>. Consequently, we get that if <span>(F^*le _K{mathcal {Z}})</span>, then: (1) if <i>X</i> is a Tychonoff space and <span>(N_F)</span> is homeomorphic to a subspace of <i>X</i>, then the space <span>(C_p^*(X))</span> of bounded continuous real-valued functions on <i>X</i> contains a complemented copy of the space <span>(c_0)</span> endowed with the pointwise topology, (2) if <i>K</i> is a compact Hausdorff space and <span>(N_F)</span> is homeomorphic to a subspace of <i>K</i>, then the Banach space <i>C</i>(<i>K</i>) of continuous real-valued functions on <i>K</i> is not a Grothendieck space. The latter result generalizes the well-known fact stating that if a compact Hausdorff space <i>K</i> contains a non-trivial convergent sequence, then the space <i>C</i>(<i>K</i>) is not Grothendieck.\u0000</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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
{"title":"Games characterizing certain families of functions","authors":"Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca","doi":"10.1007/s00153-024-00922-9","DOIUrl":"https://doi.org/10.1007/s00153-024-00922-9","url":null,"abstract":"<p>We obtain several game characterizations of Baire 1 functions between Polish spaces <i>X</i>, <i>Y</i> which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
{"title":"The extent of saturation of induced ideals","authors":"Kenta Tsukuura","doi":"10.1007/s00153-024-00919-4","DOIUrl":"https://doi.org/10.1007/s00153-024-00919-4","url":null,"abstract":"<p>We construct a model with a saturated ideal <i>I</i> over <span>({mathcal {P}}_{kappa }lambda )</span> and study the extent of saturation of <i>I</i>.\u0000</p>","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信