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Algebra and Logic最新文献

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Essential Completions of Topological Spaces 拓扑空间的基本补全
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-04-01 DOI: 10.1007/s10469-026-09821-9
Yu. L. Ershov, M. V. Schwidefsky
{"title":"Essential Completions of Topological Spaces","authors":"Yu. L. Ershov,&nbsp;M. V. Schwidefsky","doi":"10.1007/s10469-026-09821-9","DOIUrl":"10.1007/s10469-026-09821-9","url":null,"abstract":"<p>We obtain essential completions of topological T<sub>0</sub>-spaces with the help of ideal spaces. We also establish a connection between the essential completeness of function spaces and the essential completeness, as well as with the existence of approximation in the semilattice of open sets.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"144 - 159"},"PeriodicalIF":0.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631654","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
Limit Models of Ehrenfeucht Theories 埃伦费希理论的极限模型
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-27 DOI: 10.1007/s10469-026-09823-7
E. I. Khlestova
{"title":"Limit Models of Ehrenfeucht Theories","authors":"E. I. Khlestova","doi":"10.1007/s10469-026-09823-7","DOIUrl":"10.1007/s10469-026-09823-7","url":null,"abstract":"<p>Invariant properties of limit models of Ehrenfeucht theories are studied. Partial answers are obtained to the Ash–Millar question on the arithmetical decidability of models of Ehrenfeucht theories with arithmetical types.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"171 - 181"},"PeriodicalIF":0.6,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631842","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
Elementary Equivalence of Countable Atomless Boolean Algebras with Distinguished Ideal 具有可分辨理想的可数无原子布尔代数的初等等价
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-20 DOI: 10.1007/s10469-026-09826-4
J. Xiang
{"title":"Elementary Equivalence of Countable Atomless Boolean Algebras with Distinguished Ideal","authors":"J. Xiang","doi":"10.1007/s10469-026-09826-4","DOIUrl":"10.1007/s10469-026-09826-4","url":null,"abstract":"<p>We study the problem of elementary equivalence of countable atomless Boolean algebras with a distinguished nonprincipal and nondense ideal, constructed from different elementarily equivalent countable infinite atomic Boolean algebras, under the condition that both algebra and its quotient algebra by the given ideal are atomless. We prove the existence of a continuum family of such countable Boolean algebras with a distinguished ideal,</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"210 - 218"},"PeriodicalIF":0.6,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631769","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
Cartesian Extensions and Definition of the Concept of Model-Theoretic Property 模型论性质概念的笛卡儿式扩展与定义
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-17 DOI: 10.1007/s10469-026-09825-5
M. G. Peretyat’kin
{"title":"Cartesian Extensions and Definition of the Concept of Model-Theoretic Property","authors":"M. G. Peretyat’kin","doi":"10.1007/s10469-026-09825-5","DOIUrl":"10.1007/s10469-026-09825-5","url":null,"abstract":"<p>We introduce a definition of an model-theoretic property and present the set ModThProp of all model-theoretic properties concerning complete theories. We justify that the pro-posed approach corresponds to the practice of research in model theory.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"190 - 209"},"PeriodicalIF":0.6,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631649","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 Structure of Tensor Completions of 2-Nilpotent Torsion-Free Groups 2-幂零无扭群张量补全的代数结构
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-11 DOI: 10.1007/s10469-026-09819-3
M. G. Amaglobeli, A. G. Myasnikov
{"title":"Algebraic Structure of Tensor Completions of 2-Nilpotent Torsion-Free Groups","authors":"M. G. Amaglobeli,&nbsp;A. G. Myasnikov","doi":"10.1007/s10469-026-09819-3","DOIUrl":"10.1007/s10469-026-09819-3","url":null,"abstract":"<p>We study tensor completions <span>({Gotimes }_{{mathcal{N}}_{2,R}}R)</span> of finitely generated torsion-free 2-nilpotent groups <i>G</i> in the class <span>({mathcal{N}}_{2,R})</span> of all 2-nilpotent <i>R</i>-groups over a binomial domain <i>R</i>. We show that <span>({Gotimes }_{{mathcal{N}}_{2,R}}R)</span> is isomorphic to the group (<span>({Gotimes }_{mathcal{H}}R)</span>) × <i>D</i>, where <span>({Gotimes }_{mathcal{H}}R)</span> is the classical Hall <i>R</i>-completion of <i>G</i>, <i>D</i> is an Abelian <i>R</i>-group, and the direct product is a product of abstract groups (not <i>R</i>-groups!). In particular, this answers an old question of Remeslennikov about the algebraic structure of free 2-nilpotent <i>R</i>-groups in the quasivariety <span>({mathcal{N}}_{2,R})</span> (they are precisely the tensor <i>R</i>-completions of free 2-nilpotent groups).</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"127 - 134"},"PeriodicalIF":0.6,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631707","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
New Results for Algebraic Lattices 代数格的新结果
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-11 DOI: 10.1007/s10469-026-09820-w
W. Dziobiak, M. V. Schwidefsky
{"title":"New Results for Algebraic Lattices","authors":"W. Dziobiak,&nbsp;M. V. Schwidefsky","doi":"10.1007/s10469-026-09820-w","DOIUrl":"10.1007/s10469-026-09820-w","url":null,"abstract":"<p>We establish a duality between the category of algebraic lattices with complete lattice homomorphisms as morphisms and the category of join semilattices whose morphisms are join-semilattice homomorphisms possessing an additional refinement property. We draw several conclusions from this duality to benefit Lattice Theory.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"135 - 143"},"PeriodicalIF":0.6,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631708","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
Algorithmic Transformations of Partial Orders into Linearly Ordered Structures 偏序到线性有序结构的算法转换
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-07 DOI: 10.1007/s10469-026-09822-8
I. Sh. Kalimullin
{"title":"Algorithmic Transformations of Partial Orders into Linearly Ordered Structures","authors":"I. Sh. Kalimullin","doi":"10.1007/s10469-026-09822-8","DOIUrl":"10.1007/s10469-026-09822-8","url":null,"abstract":"<p>We prove that there exists a partial order having no computable copies in which any effectively interpreted linearly ordered structure has a computable copy, but there are linearly ordered structures with the same degree spectrum which are obtained by a natural algorithmic transformation not directly related to effective interpretability.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"160 - 170"},"PeriodicalIF":0.6,"publicationDate":"2026-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631809","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
Extension of Partial Automorphisms in Finite Tournament 有限竞赛中部分自同构的扩展
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-03-06 DOI: 10.1007/s10469-026-09824-6
K. Zh. Kudaibergenov
{"title":"Extension of Partial Automorphisms in Finite Tournament","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-026-09824-6","DOIUrl":"10.1007/s10469-026-09824-6","url":null,"abstract":"<p>We prove that for any finite tournament and any of its partial automorphisms there exists a finite extension of the original tournament in which this partial automorphism can be extended to a complete automorphism. An estimate for the size of this extension is given. Furthermore, it is proved that every finite tournament has a finite transitive extension, and the order of this extension is specified.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 3","pages":"182 - 189"},"PeriodicalIF":0.6,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147631852","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
Centroids of Commutatively Transitive Groups 交换传递群的质心
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-16 DOI: 10.1007/s10469-026-09818-4
A. V. Treier, I. A. Chesnokov
{"title":"Centroids of Commutatively Transitive Groups","authors":"A. V. Treier,&nbsp;I. A. Chesnokov","doi":"10.1007/s10469-026-09818-4","DOIUrl":"10.1007/s10469-026-09818-4","url":null,"abstract":"<p>We describe of centroids of commutatively transitive groups and obtain a criterion for a group to be commutatively transitive. Based on this result, we describe the structures of centroids of lamplighter groups and free solvable groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 2","pages":"113 - 125"},"PeriodicalIF":0.6,"publicationDate":"2026-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339930","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
On the Number of Minimal Elements of Ideals of Rogers Semilattices 罗杰斯半格理想中最小元的个数
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2026-02-16 DOI: 10.1007/s10469-026-09812-w
M. Kh. Faizrahmanov
{"title":"On the Number of Minimal Elements of Ideals of Rogers Semilattices","authors":"M. Kh. Faizrahmanov","doi":"10.1007/s10469-026-09812-w","DOIUrl":"10.1007/s10469-026-09812-w","url":null,"abstract":"<p>For computable families of computably enumerable sets we find sufficient conditions under which, for any n &gt; 1, the Rogers semilattices of these families have ideals containing exactly n minimal elements, each specified by positive undecidable numberings. It is shown that the Rogers semilattice of every <span>({Sigma }_{mathrm{m}}^{0})</span>-computable family, m &gt; 1, possessing a Friedberg <span>({Sigma }_{mathrm{m}}^{0})</span>-computable numbering, for any n &gt; 1 possesses an ideal that also contains exactly n minimal elements specified by positive undecidable numberings.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 1","pages":"55 - 65"},"PeriodicalIF":0.6,"publicationDate":"2026-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339929","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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