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A Criterion for P-Computability of Structures 结构P-可计算性的一个判据
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-30 DOI: 10.1007/s10469-023-09710-5
P. E. Alaev
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引用次数: 0
On the Absoluteness of ℵ1-Freeness 关于的绝对性ℵ1-自由度
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-25 DOI: 10.1007/s10469-023-09704-3
D. Herden, A. V. Pasi
{"title":"On the Absoluteness of ℵ1-Freeness","authors":"D. Herden,&nbsp;A. V. Pasi","doi":"10.1007/s10469-023-09704-3","DOIUrl":"10.1007/s10469-023-09704-3","url":null,"abstract":"<div><div><p>ℵ<sub>1</sub>-free groups, Abelian groups for which every countable subgroup is free, exhibit a number of interesting algebraic and set-theoretic properties. We will give a complete proof that the property of being ℵ<sub>1</sub>-free is absolute; that is, if an Abelian group <i>G</i> is ℵ<sub>1</sub>-free in some transitive model <b>M</b> of ZFC, then it is ℵ<sub>1</sub>-free in any transitive model of ZFC containing <i>G</i>. The absoluteness of ℵ<sub>1</sub>-freeness has the following remarkable consequence: an Abelian group <i>G</i> is ℵ<sub>1</sub>-free in some transitive model of ZFC if and only if it is (countable and) free in some model extension. This set-theoretic characterization will be a starting point for further exploring the relationship between the set-theoretic and algebraic properties of ℵ<sub>1</sub>-free groups. In particular, we will demonstrate how proofs may be dramatically simplified using model extensions for ℵ<sub>1</sub>-free groups.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"351 - 362"},"PeriodicalIF":0.5,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50512545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
Sessions of the Seminar “Algebra i Logika” “代数i Logika”研讨会
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-23 DOI: 10.1007/s10469-023-09711-4
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-023-09711-4","DOIUrl":"10.1007/s10469-023-09711-4","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"442 - 444"},"PeriodicalIF":0.5,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50506715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Class of Low Linear Orders Having Computable Presentations 一类具有可计算表示的低线性阶
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-23 DOI: 10.1007/s10469-023-09706-1
M. V. Zubkov
{"title":"A Class of Low Linear Orders Having Computable Presentations","authors":"M. V. Zubkov","doi":"10.1007/s10469-023-09706-1","DOIUrl":"10.1007/s10469-023-09706-1","url":null,"abstract":"<div><div><p>It is shown that any low linear order of the form <span>(mathcal{L})</span>+ω<sup>∗</sup>, where <span>(mathcal{L})</span> is some η-presentation, has a computable copy. This result contrasts with there being low η-presentations not having a computable copy.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"372 - 384"},"PeriodicalIF":0.5,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50506716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Complexity of the Problem of Being Equivalent to Horn Formulas. II Horn公式等价问题的复杂性。二、
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-04-28 DOI: 10.1007/s10469-023-09700-7
N. T. Kogabaev
{"title":"Complexity of the Problem of Being Equivalent to Horn Formulas. II","authors":"N. T. Kogabaev","doi":"10.1007/s10469-023-09700-7","DOIUrl":"10.1007/s10469-023-09700-7","url":null,"abstract":"<div><div><p>We look at the complexity of the existence problem for a Horn sentence equivalent to a given one. It is proved that for a signature consisting of one unary function symbol and any finite number of unary predicate symbols, the problem is computable. For a signature with at least two unary function symbols, it is stated that the problem mentioned is an m-complete <span>({sum }_{1}^{0}mathrm{set})</span>.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"318 - 327"},"PeriodicalIF":0.5,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50519448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Versions of a Local Contraction Subexponential in the Lambek Calculus Lambek微积分中局部收缩次指数的形式
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-04-26 DOI: 10.1007/s10469-023-09696-0
M. V. Valinkin
{"title":"Versions of a Local Contraction Subexponential in the Lambek Calculus","authors":"M. V. Valinkin","doi":"10.1007/s10469-023-09696-0","DOIUrl":"10.1007/s10469-023-09696-0","url":null,"abstract":"<div><div><p>The Lambek calculus was introduced as a tool for examining linguistic constructions. Then this calculus was complemented with both new connectives and structural rules like contraction, weakening, and permutation. The structural rules are allowed only for formulas under the symbol of a specific modality called exponential. The Lambek calculus itself is a noncommutative structural logic, and for arbitrary formulas, the structural rules mentioned are not allowed. The next step is the introduction of a system of subexponentials: under the symbol of such a modality, only certain structural rules are admitted. The following question arises: is it possible to formulate a system with a certain version of the local contraction rule (for formulas under subexponential) to recover the cut elimination property? We consider two approaches to solving this problem: one can both weaken the rule of introducing ! in the right-hand side of a sequent (LSCLC) and extend the local contraction rule from individual formulas to their subsequents (LMCLC). It is also worth mentioning that in commutative calculi, such a problem is missing since formulas in a sequent are allowed to be permuted (i.e, the local contraction rule coincides with the nonlocal one). The following results are proved: cut eliminability in the LMCLC and LSCLC calculi; algorithmic decidability of fragments of these calculi in which ! is allowed to be applied only to variables; algorithmic undecidability of LMCLC (for LSCLC, decidability remains an open question); correctness and absence of strong completeness of LSCLC with respect to a class of relational models; various results on equivalence for the calculi in question and the calculi with other versions of the contraction subexponential.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"271 - 287"},"PeriodicalIF":0.5,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Algebraic Properties of Subquasigroups and Construction of Finite Quasigroups 子拟群的代数性质与有限拟群的构造
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-04-24 DOI: 10.1007/s10469-023-09695-1
V. A. Artamonov, S. Chakrabarti, Sh. K. Tiwari, V. T. Markov
{"title":"Algebraic Properties of Subquasigroups and Construction of Finite Quasigroups","authors":"V. A. Artamonov,&nbsp;S. Chakrabarti,&nbsp;Sh. K. Tiwari,&nbsp;V. T. Markov","doi":"10.1007/s10469-023-09695-1","DOIUrl":"10.1007/s10469-023-09695-1","url":null,"abstract":"<div><div><p>Many important properties are identified and criteria are developed for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of proper subquasigroups in a given finite quasigroup, or finds all its proper subquasigroups. This has an important application in checking the cryptographic suitability of a quasigroup. Using arithmetic of finite fields, we introduce a binary operation to construct quasigroups of order p<sup>r</sup>. Criteria are developed under which the quasigroups mentioned have desirable cryptographic properties, such as polynomial completeness and absence of proper subquasigroups. Effective methods are given for constructing cryptographically suitable quasigroups. The efficiency of the methods is illustrated by some academic examples and implementation of all proposed algorithms in the computer algebra system <span>Singular</span>.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"251 - 270"},"PeriodicalIF":0.5,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50509475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Model Theory of Subject Domains. II 学科领域的模型理论。二、
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-04-21 DOI: 10.1007/s10469-023-09702-5
D. E. Palchunov
{"title":"Model Theory of Subject Domains. II","authors":"D. E. Palchunov","doi":"10.1007/s10469-023-09702-5","DOIUrl":"10.1007/s10469-023-09702-5","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"341 - 347"},"PeriodicalIF":0.5,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50501328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boolean Algebras Autostable Relative to n-Decidable Presentations 相对于n-可判定表示的布尔代数的自稳定
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-04-20 DOI: 10.1007/s10469-023-09698-y
M. N. Gaskova
{"title":"Boolean Algebras Autostable Relative to n-Decidable Presentations","authors":"M. N. Gaskova","doi":"10.1007/s10469-023-09698-y","DOIUrl":"10.1007/s10469-023-09698-y","url":null,"abstract":"<div><div><p>We give an algebraic description of Boolean algebras autostable relative to n-decidable presentations. Also, autostable I<sub>λ,μ</sub>-algebras are described.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"301 - 312"},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50498538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Minimal Nonzero L-Varieties of Vector Spaces Over the Field ℤ2 域上向量空间的极小非零L-变种ℤ2.
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-04-20 DOI: 10.1007/s10469-023-09699-x
A. V. Kislitsin
{"title":"Minimal Nonzero L-Varieties of Vector Spaces Over the Field ℤ2","authors":"A. V. Kislitsin","doi":"10.1007/s10469-023-09699-x","DOIUrl":"10.1007/s10469-023-09699-x","url":null,"abstract":"<div><div><p>We provide a complete description of minimal nonzero L-varieties of multiplicative vector spaces over the field ℤ<sub>2</sub>.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"313 - 317"},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50498539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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