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The Number of Countable Models of a Complete Theory and of Its Inessential Extension 完备理论的可数模型数及其非本质推广
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-05 DOI: 10.1007/s10469-025-09789-y
K. Zh. Kudaibergenov
{"title":"The Number of Countable Models of a Complete Theory and of Its Inessential Extension","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-025-09789-y","DOIUrl":"10.1007/s10469-025-09789-y","url":null,"abstract":"<p>It is proved that (<i>a</i>) there exists a complete countable theory having 2<sup><i>ω</i></sup> countable models, some inessential extension of which has <i>ω</i> countable models, and that (<i>b</i>) there exists a complete countable theory having 2<sup><i>ω</i></sup> countable models, some inessential extension of which has finitely many countable models. This gives an answer to the question of A. D. Taimanov.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"258 - 269"},"PeriodicalIF":0.6,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037265","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
Letter to the Editorial Board 给编委会的信
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-02 DOI: 10.1007/s10469-025-09793-2
M. V. Schwidefsky
{"title":"Letter to the Editorial Board","authors":"M. V. Schwidefsky","doi":"10.1007/s10469-025-09793-2","DOIUrl":"10.1007/s10469-025-09793-2","url":null,"abstract":"<p>This short note contains necessary addenda and corrections to [1].</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"294 - 299"},"PeriodicalIF":0.6,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037196","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 New Version of Orthogonality for 1-Types in Weakly o-Minimal Theories 弱o-极小理论中1型正交性的一个新版本
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-01 DOI: 10.1007/s10469-025-09791-4
B. Sh. Kulpeshov, S. V. Sudoplatov
{"title":"A New Version of Orthogonality for 1-Types in Weakly o-Minimal Theories","authors":"B. Sh. Kulpeshov,&nbsp;S. V. Sudoplatov","doi":"10.1007/s10469-025-09791-4","DOIUrl":"10.1007/s10469-025-09791-4","url":null,"abstract":"<p>We introduce a new version of orthogonality for nonalgebraic 1-types in weakly o-minimal theories, that of almost quite orthogonality. It is stated that the non almost quite orthogonality relation is an equivalence relation. The main result is a criterion for a weakly o-minimal theory of finite convexity rank with 1 &lt; I(T, ω) &lt; 2<sup>ω</sup> to have exactly 3<sup>m</sup>6<sup>l</sup> countable pairwise nonisomorphic models for some nonnegative integers m, l &lt; ω in terms of the orthogonality version presented.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"270 - 283"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037185","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
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-30 DOI: 10.1007/s10469-025-09794-1
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09794-1","DOIUrl":"10.1007/s10469-025-09794-1","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"300 - 303"},"PeriodicalIF":0.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037111","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
CEA-Operators and the Ershov Hierarchy. II cea -算子和Ershov层次。2
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-28 DOI: 10.1007/s10469-025-09788-z
M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev
{"title":"CEA-Operators and the Ershov Hierarchy. II","authors":"M. M. Arslanov,&nbsp;I. I. Batyrshin,&nbsp;M. M. Yamaleev","doi":"10.1007/s10469-025-09788-z","DOIUrl":"10.1007/s10469-025-09788-z","url":null,"abstract":"<p>We continue and finalize our research started in [Algebra and Logic, <b>63</b>, No. 3 (2024), 168–178]. It is proved that there exists a noncomputable low c.e. set <i>A</i> such that any set that is <i>CEA</i>(<i>A</i>) and 2-c.e. has a c.e. degree.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"235 - 248"},"PeriodicalIF":0.6,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037397","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 Gelfand–Kirillov Conjecture as a First-Order Formula 一阶公式的Gelfand-Kirillov猜想
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-26 DOI: 10.1007/s10469-025-09792-3
H. L. Mariano, J. Schwarz
{"title":"The Gelfand–Kirillov Conjecture as a First-Order Formula","authors":"H. L. Mariano,&nbsp;J. Schwarz","doi":"10.1007/s10469-025-09792-3","DOIUrl":"10.1007/s10469-025-09792-3","url":null,"abstract":"<p>We show that for a given (reduced) root system Σ and for any algebraically closed field k with zero characteristic, the validity of the Gelfand–Kirillov conjecture for the finite-dimensional Lie algebra <span>({mathfrak{g}}_{mathrm{k},Sigma },)</span> the sole semisimple Lie algebra over k with root system Σ, is equivalent to the provability of a certain first-order sentence in the language of rings <span>(mathcal{L})</span>(0, 1, +, ∗, −) in the theory ACF<sub>0</sub> of algebraically closed fields of zero characteristic.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"284 - 293"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037317","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
Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups 广义baumslag -孤子群普遍等价于树群
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-26 DOI: 10.1007/s10469-025-09790-5
F. A. Dudkin
{"title":"Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups","authors":"F. A. Dudkin","doi":"10.1007/s10469-025-09790-5","DOIUrl":"10.1007/s10469-025-09790-5","url":null,"abstract":"<p>A finitely generated group that acts on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (<i>GBS</i> group). Every <i>GBS</i> group is the fundamental group <i>π</i><sub>1</sub>(𝔸) of a suitable labeled graph 𝔸. If 𝔸 is a labeled tree, then we call <i>π</i><sub>1</sub>(𝔸) a tree GBS group. It is known that <i>GBS</i> groups isomorphic to tree groups are themselves tree groups. It is shown that <i>GBS</i> groups universally equivalent to tree groups do not have to be tree groups. Moreover, we give a description of all <i>GBS</i> groups that are universally equivalent to tree groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"249 - 257"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037316","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
Locally Finite Groups Containing Direct Products of Dihedral Groups 含二面体群的直积的局部有限群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-14 DOI: 10.1007/s10469-025-09785-2
A. A. Shlepkin
{"title":"Locally Finite Groups Containing Direct Products of Dihedral Groups","authors":"A. A. Shlepkin","doi":"10.1007/s10469-025-09785-2","DOIUrl":"10.1007/s10469-025-09785-2","url":null,"abstract":"<p>We prove the theorem stating the following. Let <i>G</i> be a locally finite group saturated with groups from a set 𝔐 consisting of direct products of <i>d</i> dihedral groups. Then <i>G</i> is a direct product of d groups of the form <i>B</i> ⋋ &lt;υ&gt;, where <i>B</i> is a locally cyclic group inverted by an involution υ.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"217 - 227"},"PeriodicalIF":0.4,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091051","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
Decidable Models of Ehrenfeucht Theories 埃伦费希理论的可决定模型
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-05 DOI: 10.1007/s10469-025-09779-0
P. E. Alaev, E. I. Khlestova
{"title":"Decidable Models of Ehrenfeucht Theories","authors":"P. E. Alaev,&nbsp;E. I. Khlestova","doi":"10.1007/s10469-025-09779-0","DOIUrl":"10.1007/s10469-025-09779-0","url":null,"abstract":"<p>We study countable models of Ehrenfeucht theories, i.e., complete theories with a finite number of countable models, strictly larger than 1. The notion of a primely generated model is introduced. It is proved that if all complete types of an Ehrenfeucht theory have arithmetic complexity, then any of the primely generated models of the theory possesses an arithmetically complex isomorphic presentation.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"155 - 163"},"PeriodicalIF":0.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091032","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
Wielandt 𝔛 -Subgroups Wielandt𝔛-子组
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-03 DOI: 10.1007/s10469-025-09784-3
D. O. Revin
{"title":"Wielandt 𝔛 -Subgroups","authors":"D. O. Revin","doi":"10.1007/s10469-025-09784-3","DOIUrl":"10.1007/s10469-025-09784-3","url":null,"abstract":"<p>Let 𝔛 be a nonempty class of finite groups closed under taking subgroups, homomorphic images, and extensions. We define the concept of a Wielandt 𝔛 -subgroup in an arbitrary finite group. It generalizes the concept of a submaximal 𝔛 -subgroup introduced by H. Wielandt and is key in the framework of a program proposed by Wielandt in 1979. One of the central objectives of the program is to overcome difficulties associated with the reduction to factors of a subnormal series within the natural problem of searching for maximal 𝔛 -subgroups. Wielandt 𝔛 -subgroups possess a number of properties unshareable by submaximal 𝔛 -subgroups. There is a hope that, due to these additional properties, the use of Wielandt 𝔛 -subgroups will open up new possibilities in realizing Wielandt’s program.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"201 - 216"},"PeriodicalIF":0.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091018","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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