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Model Theory of Enriched Boolean Algebras 富布尔代数的模型理论
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-09-02 DOI: 10.1007/s10469-026-09846-0
D. E. Pal’chunov, A. V. Trofimov
{"title":"Model Theory of Enriched Boolean Algebras","authors":"D. E. Pal’chunov,&nbsp;A. V. Trofimov","doi":"10.1007/s10469-026-09846-0","DOIUrl":"10.1007/s10469-026-09846-0","url":null,"abstract":"<p>We study enriched Boolean algebras. We describe subalgebras of Boolean algebras determined by fixed elements of automorphisms. We construct a continuum of superatomic Boolean algebras with a distinguished subalgebra whose elementary theories have no prime model. We investigate semigroups of elementary types of Boolean algebras with a distinguished subalgebra and of Boolean algebras with distinguished ideals.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"435 - 446"},"PeriodicalIF":0.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909571","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 Unbounded Groups of Permutations of Natural Numbers 关于自然数置换的无界群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-28 DOI: 10.1007/s10469-026-09848-y
N. M. Suchkov, A. A. Shlyopkin
{"title":"On Unbounded Groups of Permutations of Natural Numbers","authors":"N. M. Suchkov,&nbsp;A. A. Shlyopkin","doi":"10.1007/s10469-026-09848-y","DOIUrl":"10.1007/s10469-026-09848-y","url":null,"abstract":"<p>Let <i>G</i> be the group of all bounded permutations of the set of natural numbers <span>({mathbb{N}})</span>. Suppose that a group <i>H</i> contains elements <i>h</i>, <i>h</i><sub>1</sub>, . . . , <i>h</i><sub><i>n</i></sub>, . . . such that |<i>h</i>| = ∞, <span>({h}_{1}^{p})</span> = <i>h</i>, <span>({h}_{2}^{p})</span> = <i>h</i><sub>1</sub>, . . . , <span>({h}_{n}^{p})</span> = <i>h</i><sub><i>n</i>−1</sub>, . . . , where <i>p</i> is a prime number. We prove that <i>H</i> is not isomorphic to a subgroup of <i>G</i>.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"455 - 461"},"PeriodicalIF":0.4,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909647","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
The Groups G2(2m) and 3D4(23m) as Automorphism Groups of Regular Polytopes of Rank 3, 4, and 5 群G2（2m）和3D4（23m）为3、4、5阶正多面体的自同构群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-28 DOI: 10.1007/s10469-026-09844-2
R. I. Gvozdev, Ya. N. Nuzhin
{"title":"The Groups G2(2m) and 3D4(23m) as Automorphism Groups of Regular Polytopes of Rank 3, 4, and 5","authors":"R. I. Gvozdev,&nbsp;Ya. N. Nuzhin","doi":"10.1007/s10469-026-09844-2","DOIUrl":"10.1007/s10469-026-09844-2","url":null,"abstract":"<p>We prove that <i>G</i><sub>2</sub>(2<sup><i>m</i></sup>) and <sup>3</sup><i>D</i><sub>4</sub>(2<sup>3<i>m</i></sup>) are automorphism groups of regular polytopes of rank<i> n</i> = 4, 5, except for the group <sup>3</sup><i>D</i><sub>4</sub>(2<sup>3<i>m</i></sup>) when <i>n</i> = 5 and m is a power of 3. The minimal number of generating conjugate involutions whose product equals 1 is found, and the existence of new regular polytopes of rank 3 with these automorphism groups is established.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"412 - 431"},"PeriodicalIF":0.4,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909648","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
Friedberg Numberings on Admissible Sets 可容许集上的Friedberg数
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-28 DOI: 10.1007/s10469-026-09847-z
V. G. Puzarenko
{"title":"Friedberg Numberings on Admissible Sets","authors":"V. G. Puzarenko","doi":"10.1007/s10469-026-09847-z","DOIUrl":"10.1007/s10469-026-09847-z","url":null,"abstract":"<p>We consider the problem of existence of single-valued, computable, positive, and negative representations of the family of all computably enumerable subsets on admissible structures. Additionally, a description of the properties of the admissible structures under consideration is given.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"447 - 454"},"PeriodicalIF":0.4,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909582","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 Intersections of π-Hall Subgroups in a Dπ-Group with Sporadic and Alternating Composition Factors 具有偶发和交替组成因子的π-群中π-Hall子群的交点
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-27 DOI: 10.1007/s10469-026-09843-3
I. N. Belousov, V. I. Zenkov
{"title":"On Intersections of π-Hall Subgroups in a Dπ-Group with Sporadic and Alternating Composition Factors","authors":"I. N. Belousov,&nbsp;V. I. Zenkov","doi":"10.1007/s10469-026-09843-3","DOIUrl":"10.1007/s10469-026-09843-3","url":null,"abstract":"<p>We consider intersections of<i> π</i>-Hall subgroups in a finite <i>D</i><sub><i>π</i></sub>-group all of whose composition factors are sporadic or alternating groups. The main result of the paper in the case under consideration confirms Conjecture 18.31 from the Kourovka Notebook, and also gives an answer to Question 20.123(b).</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"402 - 411"},"PeriodicalIF":0.4,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909558","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 Topological Characterization of ITBM–Representable Relational Structures itbm可表示关系结构的拓扑表征
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-27 DOI: 10.1007/s10469-026-09845-1
A. S. Morozov
{"title":"A Topological Characterization of ITBM–Representable Relational Structures","authors":"A. S. Morozov","doi":"10.1007/s10469-026-09845-1","DOIUrl":"10.1007/s10469-026-09845-1","url":null,"abstract":"<p>We describe relational structures of finite signature representable by means of infinite time Blum–Shub–Smale machines in terms of Borel hierarchy on Baire and Cantor Polish spaces.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"432 - 434"},"PeriodicalIF":0.4,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909604","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
Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega 基本等价于的幂的可确定范畴模型的索引集
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-27 DOI: 10.1007/s10469-026-09842-4
N. A. Bazhenov, M. V. Zubkov, M. I. Marchuk
{"title":"Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega","authors":"N. A. Bazhenov,&nbsp;M. V. Zubkov,&nbsp;M. I. Marchuk","doi":"10.1007/s10469-026-09842-4","DOIUrl":"10.1007/s10469-026-09842-4","url":null,"abstract":"<p>A strongly constructivizable model S is decidably categorical if for any decidable copies A and B of S, there exists a computable isomorphism from A onto B. The paper investigates the complexity of families of decidably categorical models belonging to familiar finitely axiomatizable classes. For a non-zero natural number n, the index set of decidably categorical linear orders elementarily equivalent to the ordinal <i>ω</i><sup><i>n</i></sup> is an m-complete <span>({Sigma}_{2text{n}+2}^{0})</span>-set. The index set of decidably categorical structures which are elementarily equivalent to <i>ω</i><sup><i>n</i></sup>, enriched by the successor relation, is an m-complete <span>({Sigma}_{2text{n}+1}^{0})</span>-set.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"397 - 401"},"PeriodicalIF":0.4,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909605","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 Two Ways of Representation of Uncountable Structures 论不可数结构的两种表示方式
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-07-30 DOI: 10.1007/s10469-026-09838-0
A. S. Morozov
{"title":"On Two Ways of Representation of Uncountable Structures","authors":"A. S. Morozov","doi":"10.1007/s10469-026-09838-0","DOIUrl":"10.1007/s10469-026-09838-0","url":null,"abstract":"<p>An embedding of the hereditarily finite superstructure over the ordered field of real numbers into the set of reals is constructed which takes Σ-subsets to sets computable by infinite time Blum-Shub-Smale machines (ITBMs). A notion of ITBM-constructivizable structure is introduced. It is proved that constructivizability of an arbitrary algebraic structure over the ordered field of real numbers implies its ITBM-constructivizability. We obtain a theorem on the existence of ITBM-constructivizable models of the cardinality of the continuum for countable consistent theories with infinite models.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 5","pages":"330 - 348"},"PeriodicalIF":0.4,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667134","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
Conditions for Existence of Jonsson Hybrids Jonsson杂化的存在条件
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-07-28 DOI: 10.1007/s10469-026-09839-z
N. M. Mussina, I. O. Tungushbayeva, A. R. Yeshkeyev
{"title":"Conditions for Existence of Jonsson Hybrids","authors":"N. M. Mussina,&nbsp;I. O. Tungushbayeva,&nbsp;A. R. Yeshkeyev","doi":"10.1007/s10469-026-09839-z","DOIUrl":"10.1007/s10469-026-09839-z","url":null,"abstract":"<p>We investigate the existence of hybrids of Jonsson theories in various first-order languages. A general framework for hybrids is constructed, defined by ∀∃-sentences true in the Cartesian product of semantic models. For theories in the same language, examples of hybrids are provided; necessary and sufficient conditions for the existence of a hybrid in a functional signature are established; it is shown that a hybrid can inherit properties of the original theories (perfection, categoricity, stability). For theories in different languages, the existence of hybrids is proved for arbitrary enrichments of semantic models to the joint language, and an amalgam is constructed. It is shown that hybrids can differ depending on the enrichments.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 5","pages":"349 - 369"},"PeriodicalIF":0.4,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667136","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
Towards the Sharp Baer–suzuki Theorem for the π-radical: Symplectic Groups 关于π-基的Sharp Baer-suzuki定理：辛群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-07-25 DOI: 10.1007/s10469-026-09841-5
D. O. Revin
{"title":"Towards the Sharp Baer–suzuki Theorem for the π-radical: Symplectic Groups","authors":"D. O. Revin","doi":"10.1007/s10469-026-09841-5","DOIUrl":"10.1007/s10469-026-09841-5","url":null,"abstract":"<p>We study the following conjecture, which is a sharp analogue of the well-known Baer–Suzuki theorem for the π-radical of a finite group. For an arbitrary set π of primes not containing all primes, let r be the smallest prime not in π. Set m = r if r ⩽ 3 and m = r − 1 if r &gt; 3. Then, in a finite group <i>G</i>, the largest normal π-subgroup always coincides with the set of elements <i>x</i> such that any m conjugates of <i>x</i> generate a π-subgroup. To date, this conjecture has been confirmed for any finite group whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups <sup>2</sup><i>B</i><sub>2</sub>(<i>q</i>), <sup>2</sup><i>G</i><sub>2</sub>(<i>q</i>), <sup>2</sup><i>F</i><sub>4</sub>(<i>q</i>)′, <i>G</i><sub>2</sub>(<i>q</i>), or <sup>3</sup><i>D</i><sub>4</sub>(<i>q</i>). It is proved that the simple symplectic groups <i>S</i><sub>2n</sub>(<i>q</i>) can be added to this list.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 5","pages":"379 - 396"},"PeriodicalIF":0.4,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667130","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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