Archive for Mathematical Logic最新文献

Different covering numbers of compact tree ideals 紧凑树理想的不同覆盖数

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-08-16 DOI: 10.1007/s00153-024-00933-6

Jelle Mathis Kuiper, Otmar Spinas

引用次数: 0

On categoricity of scattered linear orders of constructive ranks 论构造等级的分散线性阶的分类性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-08-16 DOI: 10.1007/s00153-024-00934-5

Andrey Frolov, Maxim Zubkov

引用次数: 0

The provably total functions of basic arithmetic and its extensions 基本算术及其扩展的可证实总函数

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-08-14 DOI: 10.1007/s00153-024-00939-0

Mohammad Ardeshir, Erfan Khaniki, Mohsen Shahriari

引用次数: 0

Undecidability of indecomposable polynomial rings 不可分解多项式环的不可判定性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-08-12 DOI: 10.1007/s00153-024-00936-3

Marco Barone, Nicolás Caro-Montoya, Eudes Naziazeno

引用次数: 0

On some $$Sigma ^{B}_{0}$$ -formulae generalizing counting principles over $$V^{0}$$ 关于在 $$V^{0}$ 上概括计数原理的一些 $$Sigma ^{B}_{0}$ 公式

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-07-22 DOI: 10.1007/s00153-024-00938-1

Eitetsu Ken

{"title":"On some $$Sigma ^{B}_{0}$$ -formulae generalizing counting principles over $$V^{0}$$","authors":"Eitetsu Ken","doi":"10.1007/s00153-024-00938-1","DOIUrl":"https://doi.org/10.1007/s00153-024-00938-1","url":null,"abstract":"We formalize various counting principles and compare their strengths over (V^{0}). In particular, we conjecture the following mutual independence between:<ul>\u0000<li>\u0000a uniform version of modular counting principles and the pigeonhole principle for injections,\u0000</li>\u0000<li>\u0000a version of the oddtown theorem and modular counting principles of modulus p, where p is any natural number which is not a power of 2,\u0000</li>\u0000<li>\u0000and a version of Fisher’s inequality and modular counting principles.\u0000</li>\u0000</ul> Then, we give sufficient conditions to prove them. We give a variation of the notion of PHP-tree and k-evaluation to show that any Frege proof of the pigeonhole principle for injections admitting the uniform counting principle as an axiom scheme cannot have o(n)-evaluations. As for the remaining two, we utilize well-known notions of p-tree and k-evaluation and reduce the problems to the existence of certain families of polynomials witnessing violations of the corresponding combinatorial principles with low-degree Nullstellensatz proofs from the violation of the modular counting principle in concern.","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":"7 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784682","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 absorption’s formula definable semigroups of complete theories 论完整理论的吸收式可定义半群

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-07-20 DOI: 10.1007/s00153-024-00937-2

Mahsut Bekenov, Aida Kassatova, Anvar Nurakunov

{"title":"On absorption’s formula definable semigroups of complete theories","authors":"Mahsut Bekenov, Aida Kassatova, Anvar Nurakunov","doi":"10.1007/s00153-024-00937-2","DOIUrl":"https://doi.org/10.1007/s00153-024-00937-2","url":null,"abstract":"On the set of all first-order complete theories (T(sigma )) of a language (sigma ) we define a binary operation ({cdot }) by the rule: (Tcdot S= {{,textrm{Th},}}({Atimes Bmid Amodels T ,,text {and},, Bmodels S})) for any complete theories (T, Sin T(sigma )). The structure (langle T(sigma );cdot rangle ) forms a commutative semigroup. A subsemigroup S of (langle T(sigma );cdot rangle ) is called an absorption’s formula definable semigroup if there is a complete theory (Tin T(sigma )) such that (S=langle {Xin T(sigma )mid Xcdot T=T};cdot rangle ). In this event we say that a theory T absorbs S. In the article we show that for any absorption’s formula definable semigroup S the class ({{,textrm{Mod},}}(S)={Ain {{,textrm{Mod},}}(sigma )mid Amodels T_0,,text {for some},, T_0in S}) is axiomatizable, and there is an idempotent element (Tin S) that absorbs S. Moreover, ({{,textrm{Mod},}}(S)) is finitely axiomatizable provided T is finitely axiomatizable. We also prove that ({{,textrm{Mod},}}(S)) is a quasivariety (variety) provided T is an universal (a positive universal) theory. Some examples are provided.","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":"9 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743817","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

Intuitionistic sets and numbers: small set theory and Heyting arithmetic 直观集与数：小集理论与海廷算术

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-06-18 DOI: 10.1007/s00153-024-00935-4

Stewart Shapiro, Charles McCarty, Michael Rathjen

引用次数: 0

The Fan Theorem, its strong negation, and the determinacy of games 范式定理、其强否定和博弈的确定性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2024-06-06 DOI: 10.1007/s00153-024-00930-9

Wim Veldman

{"title":"The Fan Theorem, its strong negation, and the determinacy of games","authors":"Wim Veldman","doi":"10.1007/s00153-024-00930-9","DOIUrl":"https://doi.org/10.1007/s00153-024-00930-9","url":null,"abstract":"In the context of a weak formal theory called Basic Intuitionistic Mathematics (textsf{BIM}), we study Brouwer’s Fan Theorem and a strong negation of the Fan Theorem, Kleene’s Alternative (to the Fan Theorem). We prove that the Fan Theorem is equivalent to contrapositions of a number of intuitionistically accepted axioms of countable choice and that Kleene’s Alternative is equivalent to strong negations of these statements. We discuss finite and infinite games and introduce a constructively useful notion of determinacy. We prove that the Fan Theorem is equivalent to the Intuitionistic Determinacy Theorem. This theorem says that every subset of Cantor space (2^omega ) is, in our constructively meaningful sense, determinate. Kleene’s Alternative is equivalent to a strong negation of a special case of this theorem. We also consider a uniform intermediate value theorem and a compactness theorem for classical propositional logic. The Fan Theorem is equivalent to each of these theorems and Kleene’s Alternative is equivalent to strong negations of them. We end with a note on ‘stronger’ Fan Theorems. The paper is a sequel to Veldman (Arch Math Logic 53:621–693, 2014).","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":"6 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551727","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