Journal of Mathematical Logic最新文献_第9页

On uniform definability of types over finite sets for NIP formulas 有限集上NIP公式类型的一致可定义性

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-04-23 DOI: 10.1142/s021906132150015x

Shlomo Eshel, Itay Kaplan

引用次数: 6

Abraham-Rubin-Shelah open colorings and a large continuum 亚伯拉罕-鲁宾-希拉开放着色和大连续体

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-04-23 DOI: 10.1142/S0219061321500276

Thomas Gilton, I. Neeman

引用次数: 4

Controlling cardinal characteristics without adding reals 不加实量而控制基本特性

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-04-04 DOI: 10.1142/S0219061321500185

M. Goldstern, Jakob Kellner, D. Mej'ia, S. Shelah

引用次数: 9

Coarse groups, and the isomorphism problem for oligomorphic groups 粗糙群，以及少纯群的同构问题

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-03-20 DOI: 10.1142/s021906132150029x

A. Nies, Philipp Schlicht, K. Tent

{"title":"Coarse groups, and the isomorphism problem for oligomorphic groups","authors":"A. Nies, Philipp Schlicht, K. Tent","doi":"10.1142/s021906132150029x","DOIUrl":"https://doi.org/10.1142/s021906132150029x","url":null,"abstract":"Let [Formula: see text] denote the topological group of permutations of the natural numbers. A closed subgroup [Formula: see text] of [Formula: see text] is called oligomorphic if for each [Formula: see text], its natural action on [Formula: see text]-tuples of natural numbers has only finitely many orbits. We study the complexity of the topological isomorphism relation on the oligomorphic subgroups of [Formula: see text] in the setting of Borel reducibility between equivalence relations on Polish spaces. Given a closed subgroup [Formula: see text] of [Formula: see text], the coarse group [Formula: see text] is the structure with domain the cosets of open subgroups of [Formula: see text], and a ternary relation [Formula: see text]. This structure derived from [Formula: see text] was introduced in [A. Kechris, A. Nies and K. Tent, The complexity of topological group isomorphism, J. Symbolic Logic 83(3) (2018) 1190–1203, Sec. 3.3]. If [Formula: see text] has only countably many open subgroups, then [Formula: see text] is a countable structure. Coarse groups form our main tool in studying such closed subgroups of [Formula: see text]. We axiomatize them abstractly as structures with a ternary relation. For the oligomorphic groups, and also the profinite groups, we set up a Stone-type duality between the groups and the corresponding coarse groups. In particular, we can recover an isomorphic copy of [Formula: see text] from its coarse group in a Borel fashion. We use this duality to show that the isomorphism relation for oligomorphic subgroups of [Formula: see text] is Borel reducible to a Borel equivalence relation with all classes countable. We show that the same upper bound applies to the larger class of closed subgroups of [Formula: see text] that are topologically isomorphic to oligomorphic groups.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"PP 1","pages":"2150029:1-2150029:31"},"PeriodicalIF":0.9,"publicationDate":"2019-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84860043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 2

Uncountable structures are not classifiable up to bi-embeddability 不可数结构在双嵌入性范围内是不可分类的

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-03-18 DOI: 10.1142/S0219061320500014

F. Calderoni, H. Mildenberger, L. Ros

{"title":"Uncountable structures are not classifiable up to bi-embeddability","authors":"F. Calderoni, H. Mildenberger, L. Ros","doi":"10.1142/S0219061320500014","DOIUrl":"https://doi.org/10.1142/S0219061320500014","url":null,"abstract":"Answering some of the main questions from [L. Motto Ros, The descriptive set-theoretical complexity of the embeddability relation on models of large size, Ann. Pure Appl. Logic 164(12) (2013) 1454–1492], we show that whenever [Formula: see text] is a cardinal satisfying [Formula: see text], then the embeddability relation between [Formula: see text]-sized structures is strongly invariantly universal, and hence complete for ([Formula: see text]-)analytic quasi-orders. We also prove that in the above result we can further restrict our attention to various natural classes of structures, including (generalized) trees, graphs, or groups. This fully generalizes to the uncountable case the main results of [A. Louveau and C. Rosendal, Complete analytic equivalence relations, Trans. Amer. Math. Soc. 357(12) (2005) 4839–4866; S.-D. Friedman and L. Motto Ros, Analytic equivalence relations and bi-embeddability, J. Symbolic Logic 76(1) (2011) 243–266; J. Williams, Universal countable Borel quasi-orders, J. Symbolic Logic 79(3) (2014) 928–954; F. Calderoni and L. Motto Ros, Universality of group embeddability, Proc. Amer. Math. Soc. 146 (2018) 1765–1780].","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"28 1","pages":"2050001"},"PeriodicalIF":0.9,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79202330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 4

Tameness, powerful images, and large cardinals 温顺，强大的形象，和大枢机

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-02-26 DOI: 10.1142/s0219061320500245

Will Boney, M. Lieberman

引用次数: 2

Mice with finitely many Woodin cardinals from optimal determinacy hypotheses 基于最优确定性假设的具有有限多个伍丁基数的小鼠

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-02-15 DOI: 10.1142/S0219061319500132

Sandra Müller, R. Schindler, W. Woodin

引用次数: 23

From noncommutative diagrams to anti-elementary classes 从非交换图到反初等类

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-01-31 DOI: 10.1142/S0219061321500112

F. Wehrung

{"title":"From noncommutative diagrams to anti-elementary classes","authors":"F. Wehrung","doi":"10.1142/S0219061321500112","DOIUrl":"https://doi.org/10.1142/S0219061321500112","url":null,"abstract":"Anti-elementarity is a strong way of ensuring that a class of structures , in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form L ∞λ. We prove that many naturally defined classes are anti-elementary, including the following: • the class of all lattices of finitely generated convex l-subgroups of members of any class of l-groups containing all Archimedean l-groups; • the class of all semilattices of finitely generated l-ideals of members of any nontrivial quasivariety of l-groups; • the class of all Stone duals of spectra of MV-algebras-this yields a negative solution for the MV-spectrum Problem; • the class of all semilattices of finitely generated two-sided ideals of rings; • the class of all semilattices of finitely generated submodules of modules; • the class of all monoids encoding the nonstable K_0-theory of von Neumann regular rings, respectively C*-algebras of real rank zero; • (assuming arbitrarily large Erd˝os cardinals) the class of all coordinatizable sectionally complemented modular lattices with a large 4-frame. The main underlying principle is that under quite general conditions, for a functor Φ : A → B, if there exists a non-commutative diagram D of A, indexed by a common sort of poset called an almost join-semilattice, such that • Φ D^I is a commutative diagram for every set I, • Φ D is not isomorphic to Φ X for any commutative diagram X in A, then the range of Φ is anti-elementary.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"45 1","pages":"2150011:1-2150011:56"},"PeriodicalIF":0.9,"publicationDate":"2019-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77701518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 8

The Ramsey theory of Henson graphs 汉森图的拉姆齐理论

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-01-20 DOI: 10.1142/s0219061322500180

Natasha Dobrinen

{"title":"The Ramsey theory of Henson graphs","authors":"Natasha Dobrinen","doi":"10.1142/s0219061322500180","DOIUrl":"https://doi.org/10.1142/s0219061322500180","url":null,"abstract":"For $kge 3$, the Henson graph $mathcal{H}_k$ is the analogue of the Rado graph in which $k$-cliques are forbidden. Building on the author's result for $mathcal{H}_3$, we prove that for each $kge 4$, $mathcal{H}_k$ has finite big Ramsey degrees: To each finite $k$-clique-free graph $G$, there corresponds an integer $T(G,mathcal{H}_k)$ such that for any coloring of the copies of $G$ in $mathcal{H}_k$ into finitely many colors, there is a subgraph of $mathcal{H}_k$, again isomorphic to $mathcal{H}_k$, in which the coloring takes no more than $T(G, mathcal{H}_k)$ colors. Prior to this article, the Ramsey theory of $mathcal{H}_k$ for $kge 4$ had only been resolved for vertex colorings by El-Zahar and Sauer in 1989. We develop a unified framework for coding copies of $mathcal{H}_k$ into a new class of trees, called strong $mathcal{H}_k$-coding trees, and prove Ramsey theorems for these trees, forming a family of Halpern-Lauchli and Milliken-style theorems which are applied to deduce finite big Ramsey degrees. The approach here streamlines the one in cite{DobrinenH_317} for $mathcal{H}_3$ and provides a general methodology opening further study of big Ramsey degrees for homogeneous structures with forbidden configurations. The results have bearing on topological dynamics via work of Kechris, Pestov, and Todorcevic and recent work of Zucker.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"162 1","pages":"2250018:1-2250018:88"},"PeriodicalIF":0.9,"publicationDate":"2019-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83856817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 16

Definable V-topologies, Henselianity and NIP 可定义v -拓扑、Henselianity和NIP

IF 0.9 1区数学

Journal of Mathematical Logic Pub Date : 2019-01-17 DOI: 10.1142/s0219061320500087

Yatir Halevi, Assaf Hasson, Franziska Jahnke

引用次数: 19