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Modification and Correction of Medvedev’s Example of a Solvable Alternative Algebra 对Medvedev可解替代代数例子的修正
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-09-06 DOI: 10.1007/s10469-023-09709-y
I. P. Shestakov
{"title":"Modification and Correction of Medvedev’s Example of a Solvable Alternative Algebra","authors":"I. P. Shestakov","doi":"10.1007/s10469-023-09709-y","DOIUrl":"10.1007/s10469-023-09709-y","url":null,"abstract":"<div><div><p>Yu. A. Medvedev [Algebra and Logic, <b>19</b>, No. 3, 191—201 (1980)] constructed an example of alternative algebra that he used to prove that a certain variety of alternative algebras possess the non-Specht property over a field of characteristic 2. Though his result concerned the characteristic 2 case, the example was claimed to be alternative over an arbitrary field, and it was later used by V. T. Filippov in a series of papers. Unfortunately, Medvedev’s example is in fact not alternative in any characteristic. Therefore, whether the variety considered by Medvedev has the non-Specht property is still not clear. Moreover, the results of Filippov’s papers, in which Medvedev’s example was used, also become questionable. We construct new examples and employ them to prove that the results of Filippov remain true.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"420 - 436"},"PeriodicalIF":0.5,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50457125","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
Partial Hopf–Galois Theory 部分Hopf–Galois理论
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-09-04 DOI: 10.1007/s10469-023-09707-0
F. Castro, D. Freitas, A. Paques, G. Quadros, T. Tamusiunas
{"title":"Partial Hopf–Galois Theory","authors":"F. Castro,&nbsp;D. Freitas,&nbsp;A. Paques,&nbsp;G. Quadros,&nbsp;T. Tamusiunas","doi":"10.1007/s10469-023-09707-0","DOIUrl":"10.1007/s10469-023-09707-0","url":null,"abstract":"<div><div><p>A partial Hopf–Galois theory is developed for partial H-module algebras, and we recover analogs of classical results for Hopf algebras.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"385 - 406"},"PeriodicalIF":0.5,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50451043","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
Pre-Minimal Pairs and Homogeneous Valuations 预极小对与齐次估值
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-30 DOI: 10.1007/s10469-023-09705-2
Yu. L. Ershov
{"title":"Pre-Minimal Pairs and Homogeneous Valuations","authors":"Yu. L. Ershov","doi":"10.1007/s10469-023-09705-2","DOIUrl":"10.1007/s10469-023-09705-2","url":null,"abstract":"<div><div><p>We offer for consideration and study the concept of a pre-minimal pair. Also we examine extensions of valuations of a field <i>F</i> to valuations of the rational function field <i>F</i>(<i>x</i>) in one variable.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"363 - 371"},"PeriodicalIF":0.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50524839","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
Dynamic Temporal Logical Operations in Multi-Agent Logics 多Agent逻辑中的动态时态逻辑运算
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-30 DOI: 10.1007/s10469-023-09708-z
V. V. Rybakov
{"title":"Dynamic Temporal Logical Operations in Multi-Agent Logics","authors":"V. V. Rybakov","doi":"10.1007/s10469-023-09708-z","DOIUrl":"10.1007/s10469-023-09708-z","url":null,"abstract":"<div><div><p>We study temporal multi-agent logics using a new approach to defining time for individual agents. It is assumed that in any time state each agent (in a sense) generates its own future time, which will only be available for analysis in the future. That is, the defined time interval depends both on the agent and on the initial state where the agent starts to act. It is also assumed that the agent may have intervals of forgotten (lost) time. We investigate problems of unification and problems of computable recognizing admissible inference rules. An algorithm is found for solving these problems based on the construction of a finite computable set of formulas which is a complete set of unifiers. We use the technique of projective formulas developed by S. Ghilardi. It is proved that any unifiable formula is in fact projective and an algorithm is constructed which creates its projective unifier. Thereby we solve the unification problem, and based at this, find the solution to the open problem of computable recognizing admissible inference rules.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"407 - 419"},"PeriodicalIF":0.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50524838","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 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
{"title":"A Criterion for P-Computability of Structures","authors":"P. E. Alaev","doi":"10.1007/s10469-023-09710-5","DOIUrl":"10.1007/s10469-023-09710-5","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"437 - 441"},"PeriodicalIF":0.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50524837","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 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
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