Archive for Mathematical Logic最新文献_第8页

Towers, mad families, and unboundedness 塔楼、疯狂的家庭和无边界。

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-02-12 DOI: 10.1007/s00153-023-00861-x

Vera Fischer, Marlene Koelbing, Wolfgang Wohofsky

引用次数: 2

Involutive symmetric Gödel spaces, their algebraic duals and logic 对合对称Gödel空间及其代数对偶与逻辑

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-02-10 DOI: 10.1007/s00153-023-00866-6

A. Di Nola, R. Grigolia, G. Vitale

{"title":"Involutive symmetric Gödel spaces, their algebraic duals and logic","authors":"A. Di Nola, R. Grigolia, G. Vitale","doi":"10.1007/s00153-023-00866-6","DOIUrl":"10.1007/s00153-023-00866-6","url":null,"abstract":"<div>It is introduced a new algebra ((A, otimes , oplus , *, rightharpoonup , 0, 1)) called (L_PG)-algebra if ((A, otimes , oplus , *, 0, 1)) is (L_P)-algebra (i.e. an algebra from the variety generated by perfect MV-algebras) and ((A,rightharpoonup , 0, 1)) is a Gödel algebra (i.e. Heyting algebra satisfying the identity ((x rightharpoonup y ) vee (y rightharpoonup x ) =1)). The lattice of congruences of an (L_PG) -algebra ((A, otimes , oplus , *, rightharpoonup , 0, 1)) is isomorphic to the lattice of Skolem filters (i.e. special type of MV-filters) of the MV-algebra ((A, otimes , oplus , *, 0, 1)). The variety (mathbf {L_PG}) of (L_PG) -algebras is generated by the algebras ((C, otimes , oplus , *, rightharpoonup , 0, 1)) where ((C, otimes , oplus , *, 0, 1)) is Chang MV-algebra. Any (L_PG) -algebra is bi-Heyting algebra. The set of theorems of the logic (L_PG) is recursively enumerable. Moreover, we describe finitely generated free (L_PG)-algebras.</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"789 - 809"},"PeriodicalIF":0.3,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00866-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46294733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Ranks based on strong amalgamation Fraïssé classes 基于强合并的等级Fraïssé等级

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-02-02 DOI: 10.1007/s00153-023-00864-8

Vincent Guingona, Miriam Parnes

引用次数: 2

A criterion for the strong cell decomposition property 强细胞分解性的判据

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2023-01-31 DOI: 10.1007/s00153-023-00862-w

Somayyeh Tari

{"title":"A criterion for the strong cell decomposition property","authors":"Somayyeh Tari","doi":"10.1007/s00153-023-00862-w","DOIUrl":"10.1007/s00153-023-00862-w","url":null,"abstract":"<div>Let ( {mathcal {M}}=(M, <, ldots ) ) be a weakly o-minimal structure. Assume that ( {mathcal {D}}ef({mathcal {M}})) is the collection of all definable sets of ( {mathcal {M}} ) and for any ( min {mathbb {N}} ), ( {mathcal {D}}ef_m({mathcal {M}}) ) is the collection of all definable subsets of ( M^m ) in ( {mathcal {M}} ). We show that the structure ( {mathcal {M}} ) has the strong cell decomposition property if and only if there is an o-minimal structure ( {mathcal {N}} ) such that ( {mathcal {D}}ef({mathcal {M}})={Ycap M^m: min {mathbb {N}}, Yin {mathcal {D}}ef_m({mathcal {N}})} ). Using this result, we prove that: (a) Every induced structure has the strong cell decomposition property. (b) The structure ( {mathcal {M}} ) has the strong cell decomposition property if and only if the weakly o-minimal structure ( {mathcal {M}}^*_M ) has the strong cell decomposition property. Also we examine some properties of non-valuational weakly o-minimal structures in the context of weakly o-minimal structures admitting the strong cell decomposition property.</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 7-8","pages":"871 - 887"},"PeriodicalIF":0.3,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45685313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Some implications of Ramsey Choice for families of (varvec{n})-element sets Ramsey选择对（varvec｛n｝）-元素集族的一些启示

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-12-16 DOI: 10.1007/s00153-022-00860-4

Lorenz Halbeisen, Salome Schumacher

{"title":"Some implications of Ramsey Choice for families of (varvec{n})-element sets","authors":"Lorenz Halbeisen, Salome Schumacher","doi":"10.1007/s00153-022-00860-4","DOIUrl":"10.1007/s00153-022-00860-4","url":null,"abstract":"<div>For (nin omega ), the weak choice principle (textrm{RC}_n) is defined as follows:<blockquote><div>\u0000 For every infinite set X there is an infinite subset (Ysubseteq X) with a choice function on ([Y]^n:={zsubseteq Y:|z|=n}).\u0000 </div></blockquote>The choice principle (textrm{C}_n^-) states the following:<blockquote><div>\u0000 For every infinite family of n-element sets, there is an infinite subfamily ({mathcal {G}}subseteq {mathcal {F}}) with a choice function.\u0000 </div></blockquote>The choice principles (textrm{LOC}_n^-) and (textrm{WOC}_n^-) are the same as (textrm{C}_n^-), but we assume that the family ({mathcal {F}}) is linearly orderable (for (textrm{LOC}_n^-)) or well-orderable (for (textrm{WOC}_n^-)). In the first part of this paper, for (m,nin omega ) we will give a full characterization of when the implication (textrm{RC}_mRightarrow textrm{WOC}_n^-) holds in ({textsf {ZF}}). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that (textrm{RC}_5Rightarrow textrm{LOC}_5^-) and that (textrm{RC}_6Rightarrow textrm{C}_3^-), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that (textrm{RC}_6Rightarrow textrm{C}_9^-) and that (textrm{RC}_7Rightarrow textrm{LOC}_7^-).\u0000</div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"703 - 733"},"PeriodicalIF":0.3,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-022-00860-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50058165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Independent families and some notions of finiteness 独立的家庭和一些有限的概念

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-12-14 DOI: 10.1007/s00153-022-00858-y

Eric Hall, Kyriakos Keremedis

引用次数: 1

Glivenko sequent classes and constructive cut elimination in geometric logics 几何逻辑中的Glivenko序类与构造切消

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-12-08 DOI: 10.1007/s00153-022-00857-z

Giulio Fellin, Sara Negri, Eugenio Orlandelli

引用次数: 2

The structure of (kappa )-maximal cofinitary groups (kappa ) -极大共缘群的结构

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-12-04 DOI: 10.1007/s00153-022-00859-x

Vera Fischer, Corey Bacal Switzer

{"title":"The structure of (kappa )-maximal cofinitary groups","authors":"Vera Fischer, Corey Bacal Switzer","doi":"10.1007/s00153-022-00859-x","DOIUrl":"10.1007/s00153-022-00859-x","url":null,"abstract":"<div>We study (kappa )-maximal cofinitary groups for (kappa ) regular uncountable, (kappa = kappa ^{<kappa }). Revisiting earlier work of Kastermans and building upon a recently obtained higher analogue of Bell’s theorem, we show that: <ol>\u0000 <li>\u0000 (1)\u0000 \u0000 Any (kappa )-maximal cofinitary group has ({<}kappa ) many orbits under the natural group action of (S(kappa )) on (kappa ).\u0000 \u0000 </li>\u0000 <li>\u0000 (2)\u0000 \u0000 If (mathfrak {p}(kappa ) = 2^kappa ) then any partition of (kappa ) into less than (kappa ) many sets can be realized as the orbits of a (kappa )-maximal cofinitary group.\u0000 \u0000 </li>\u0000 <li>\u0000 (3)\u0000 \u0000 For any regular (lambda > kappa ) it is consistent that there is a (kappa )-maximal cofinitary group which is universal for groups of size ({<}2^kappa = lambda ). If we only require the group to be universal for groups of size (kappa ) then this follows from (mathfrak {p}(kappa ) = 2^kappa ).\u0000\u0000 \u0000 </li>\u0000 </ol></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"62 5-6","pages":"641 - 655"},"PeriodicalIF":0.3,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-022-00859-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50007773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Correction to: Generalization of Shapiro’s theorem to higher arities and noninjective notations 修正：Shapiro定理到更高arities和非射符号的推广

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-11-09 DOI: 10.1007/s00153-022-00855-1

Dariusz Kalociński, Michał Wrocławski

引用次数: 0

Generic existence of interval P-points 区间p点的一般存在性

IF 0.3 4区数学

Archive for Mathematical Logic Pub Date : 2022-11-07 DOI: 10.1007/s00153-022-00853-3

Jialiang He, Renling Jin, Shuguo Zhang

引用次数: 0