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Journal of Mathematical Logic最新文献

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On the existence of small antichains for definable quasi-orders 关于可定义拟序的小反链的存在性
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2020-02-15 DOI: 10.1142/s0219061321500057
Raphaël Carroy, B. D. Miller, Zolt'an Vidny'anszky
{"title":"On the existence of small antichains for definable quasi-orders","authors":"Raphaël Carroy, B. D. Miller, Zolt'an Vidny'anszky","doi":"10.1142/s0219061321500057","DOIUrl":"https://doi.org/10.1142/s0219061321500057","url":null,"abstract":"We generalize Kada’s definable strengthening of Dilworth’s characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82342216","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: 1
Forking and dividing in fields with several orderings and valuations 在具有多个排序和赋值的域中进行分叉和划分
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2020-01-08 DOI: 10.1142/S0219061321500252
Will Johnson
{"title":"Forking and dividing in fields with several orderings and valuations","authors":"Will Johnson","doi":"10.1142/S0219061321500252","DOIUrl":"https://doi.org/10.1142/S0219061321500252","url":null,"abstract":"We consider existentially closed fields with several orderings, valuations, and [Formula: see text]-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Moreover, forking agrees with dividing, and forking can be characterized in terms of forking in ACVF, RCF, and [Formula: see text]CF.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74963473","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: 3
Logical laws for short existential monadic second-order sentences about graphs 关于图的存在一元二阶短句的逻辑规律
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-12-12 DOI: 10.1142/s0219061320500075
M. Zhukovskii
{"title":"Logical laws for short existential monadic second-order sentences about graphs","authors":"M. Zhukovskii","doi":"10.1142/s0219061320500075","DOIUrl":"https://doi.org/10.1142/s0219061320500075","url":null,"abstract":"In 2001, Le Bars proved that there exists an existential monadic second-order (EMSO) sentence such that the probability that it is true on [Formula: see text] does not converge and conjectured that, for EMSO sentences with two first-order variables, the zero–one law holds. In this paper, we prove that the conjecture fails for [Formula: see text], and give new examples of sentences with fewer variables without convergence (even for [Formula: see text]).","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72525938","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
Sigma-Prikry forcing II: Iteration Scheme Sigma-Prikry强迫II:迭代方案
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-12-06 DOI: 10.1142/S0219061321500197
Alejandro Poveda, A. Rinot, Dima Sinapova
{"title":"Sigma-Prikry forcing II: Iteration Scheme","authors":"Alejandro Poveda, A. Rinot, Dima Sinapova","doi":"10.1142/S0219061321500197","DOIUrl":"https://doi.org/10.1142/S0219061321500197","url":null,"abstract":"In Part I of this series [5], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We proved that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a nonreflecting stationary set [Formula: see text], there exists a corresponding [Formula: see text]-Prikry poset that projects to [Formula: see text] and kills the stationarity of [Formula: see text]. In this paper, we develop a general scheme for iterating [Formula: see text]-Prikry posets, as well as verify that the Extender-based Prikry forcing is [Formula: see text]-Prikry. As an application, we blow-up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all nonreflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73078895","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: 5
Knaster and friends II: The C-sequence number Knaster和他的朋友们II: c序列
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-12-06 DOI: 10.1142/s0219061321500021
C. Lambie-Hanson, A. Rinot
{"title":"Knaster and friends II: The C-sequence number","authors":"C. Lambie-Hanson, A. Rinot","doi":"10.1142/s0219061321500021","DOIUrl":"https://doi.org/10.1142/s0219061321500021","url":null,"abstract":"Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the [Formula: see text]-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of [Formula: see text] and independence results about the [Formula: see text]-sequence number and its relationship with large cardinals, stationary reflection, and square principles. We then introduce and study the more general [Formula: see text]-sequence spectrum and uncover some tight connections between the [Formula: see text]-sequence spectrum and the strong coloring principle [Formula: see text], introduced in Part I of this series.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74292955","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: 11
Notice of Retraction: Pseudofinite difference field 撤回通知：伪有限差分域
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-10-24 DOI: 10.1142/s0219061319930012
Tingxiang Zou
{"title":"Notice of Retraction: Pseudofinite difference field","authors":"Tingxiang Zou","doi":"10.1142/s0219061319930012","DOIUrl":"https://doi.org/10.1142/s0219061319930012","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s0219061319930012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46059739","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: 0
On possible restrictions of the null ideal 零理想的可能约束
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-10-02 DOI: 10.1142/S0219061319500089
Ashutosh Kumar, S. Shelah
{"title":"On possible restrictions of the null ideal","authors":"Ashutosh Kumar, S. Shelah","doi":"10.1142/S0219061319500089","DOIUrl":"https://doi.org/10.1142/S0219061319500089","url":null,"abstract":"We prove that the null ideal restricted to a non-null set of reals could be isomorphic to a variety of sigma ideals. Using this, we show that the following are consistent: (1) There is a non-null subset of plane each of whose non-null subsets contains three collinear points. (2) There is a partition of a non-null set of reals into null sets, each of size [Formula: see text], such that every transversal of this partition is null.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80431170","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: 6
A descriptive Main Gap Theorem 一个描述性的主间隙定理
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-09-17 DOI: 10.1142/s0219061320500257
Francesco Mangraviti, L. Ros
{"title":"A descriptive Main Gap Theorem","authors":"Francesco Mangraviti, L. Ros","doi":"10.1142/s0219061320500257","DOIUrl":"https://doi.org/10.1142/s0219061320500257","url":null,"abstract":"Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230(1081) (2014) 80, Chap. 7], we show that there is a tight connection between the depth of a classifiable shallow theory [Formula: see text] and the Borel rank of the isomorphism relation [Formula: see text] on its models of size [Formula: see text], for [Formula: see text] any cardinal satisfying [Formula: see text]. This is achieved by establishing a link between said rank and the [Formula: see text]-Scott height of the [Formula: see text]-sized models of [Formula: see text], and yields to the following descriptive set-theoretical analog of Shelah’s Main Gap Theorem: Given a countable complete first-order theory [Formula: see text], either [Formula: see text] is Borel with a countable Borel rank (i.e. very simple, given that the length of the relevant Borel hierarchy is [Formula: see text]), or it is not Borel at all. The dividing line between the two situations is the same as in Shelah’s theorem, namely that of classifiable shallow theories. We also provide a Borel reducibility version of the above theorem, discuss some limitations to the possible (Borel) complexities of [Formula: see text], and provide a characterization of categoricity of [Formula: see text] in terms of the descriptive set-theoretical complexity of [Formula: see text].","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77037323","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: 3
Bounds on Scott ranks of some polish metric spaces 一些波兰度量空间的斯科特阶的边界
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-06-11 DOI: 10.1142/s021906132150001x
William Chan
{"title":"Bounds on Scott ranks of some polish metric spaces","authors":"William Chan","doi":"10.1142/s021906132150001x","DOIUrl":"https://doi.org/10.1142/s021906132150001x","url":null,"abstract":"If [Formula: see text] is a proper Polish metric space and [Formula: see text] is any countable dense submetric space of [Formula: see text], then the Scott rank of [Formula: see text] in the natural first-order language of metric spaces is countable and in fact at most [Formula: see text], where [Formula: see text] is the Church–Kleene ordinal of [Formula: see text] (construed as a subset of [Formula: see text]) which is the least ordinal with no presentation on [Formula: see text] computable from [Formula: see text]. If [Formula: see text] is a rigid Polish metric space and [Formula: see text] is any countable dense submetric space, then the Scott rank of [Formula: see text] is countable and in fact less than [Formula: see text].","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83349892","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
Co-theory of sorted profinite groups for PAC structures PAC结构的分选无限群共论
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2019-05-23 DOI: 10.1142/s0219061322500301
D. Hoffmann, Junguk Lee
{"title":"Co-theory of sorted profinite groups for PAC structures","authors":"D. Hoffmann, Junguk Lee","doi":"10.1142/s0219061322500301","DOIUrl":"https://doi.org/10.1142/s0219061322500301","url":null,"abstract":"We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove a \"weak independence theorem\" for PAC substructures of an ambient structure with nfcp and property B(3). Fourth, we describe Kim-dividing in these PAC substructures and show several results related to NSOP. Fifth, we characterize the algebraic closure in PAC structures.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77095562","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: 5
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