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Covering at limit cardinals of K 覆盖K的极限基数
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-02-10 DOI: 10.1142/s0219061323500046
W. Mitchell, Ernest Schimmerling
{"title":"Covering at limit cardinals of K","authors":"W. Mitchell, Ernest Schimmerling","doi":"10.1142/s0219061323500046","DOIUrl":"https://doi.org/10.1142/s0219061323500046","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48117338","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
The degree of nonminimality is at most 2 非极小性的程度最多为2
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-01-01 DOI: 10.1142/S0219061322500313
J. Freitag, Rémi Jaoui, Rahim Moosa
{"title":"The degree of nonminimality is at most 2","authors":"J. Freitag, Rémi Jaoui, Rahim Moosa","doi":"10.1142/S0219061322500313","DOIUrl":"https://doi.org/10.1142/S0219061322500313","url":null,"abstract":". It is shown that if p ∈ S ( A ) is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a 1 ,a 2 such that p has a nonalgebraic forking extension over Aa 1 a 2 . Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over Aa 1 . The results are also formulated in a more general setting.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80276776","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
More definable combinatorics around the first and second uncountable cardinals 围绕第一和第二不可数基数的更多可定义组合
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-01-01 DOI: 10.1142/S0219061322500295
William Chan, Stephen Jackson, Nam Trang
{"title":"More definable combinatorics around the first and second uncountable cardinals","authors":"William Chan, Stephen Jackson, Nam Trang","doi":"10.1142/S0219061322500295","DOIUrl":"https://doi.org/10.1142/S0219061322500295","url":null,"abstract":"Assume ZF+AD. The following two continuity results for functions on certain subsets of P(ω1) and P(ω2) will be shown: For every < ω1 and function Φ : [ω1] → ω1, there is a club C ⊆ ω1 and a ζ < so that for all f, g ∈ [C] ∗, if f ζ = g ζ and sup(f) = sup(g), then Φ(f) = Φ(g). For every < ω2 and function Φ : [ω2] → ω2, there is an ω-club C ⊆ ω2 and a ζ < so that for all f, g ∈ [C] ∗, if f ζ = g ζ and sup(f) = sup(g), then Φ(f) = Φ(g). The previous two continuity results will be used to distinguish cardinals below P(ω2): |[ω1] | < |[ω1]1 |. |[ω2] | < |ω2]1 | < |[ω2]1 | < |[ω2]2 |. ¬(|[ω1]1 | ≤ [ω2] |). ¬(|[ω1]1 | ≤ ([ω2]1 |). [ω1] has the Jónsson property: That is, for every Φ : ([ω1]) → [ω1] , there is an X ⊆ [ω1] with |X| = |[ω1] | so that Φ[","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82602286","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
On piecewise hyperdefinable groups 关于分段超可定义群
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-12-17 DOI: 10.1142/s0219061322500271
A. Rodriguez Fanlo
{"title":"On piecewise hyperdefinable groups","authors":"A. Rodriguez Fanlo","doi":"10.1142/s0219061322500271","DOIUrl":"https://doi.org/10.1142/s0219061322500271","url":null,"abstract":"The aim of this paper is to generalize and improve two of the main model-theoretic results of “Stable group theory and approximate subgroups” by Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence of Lie models. The second one is the Stabilizer Theorem. In the process, a systematic study of the structure of piecewise hyperdefinable sets is developed. In particular, we show the most significant properties of their logic topologies.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64341575","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
Degrees of categoricity and treeable degrees 分类度和可树度
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-09-09 DOI: 10.1142/s0219061324500028
Barbara F. Csima, D. Rossegger
{"title":"Degrees of categoricity and treeable degrees","authors":"Barbara F. Csima, D. Rossegger","doi":"10.1142/s0219061324500028","DOIUrl":"https://doi.org/10.1142/s0219061324500028","url":null,"abstract":"We give a characterization of the strong degrees of categoricity of computable structures greater or equal to $mathbf 0''$. They are precisely the emph{treeable} degrees -- the least degrees of paths through computable trees -- that compute $mathbf 0''$. As a corollary, we obtain several new examples of degrees of categoricity. Among them we show that every degree $mathbf d$ with $mathbf 0^{(alpha)}leq mathbf dleq mathbf 0^{(alpha+1)}$ for $alpha$ a computable ordinal greater than $2$ is the strong degree of categoricity of a rigid structure. Using quite different techniques we show that every degree $mathbf d$ with $mathbf 0'leq mathbf dleq mathbf 0''$ is the strong degree of categoricity of a structure. Together with the above example this answers a question of Csima and Ng. To complete the picture we show that there is a degree $mathbf d$ with $mathbf 0'<mathbf d<mathbf 0''$ that is not the degree of categoricity of a rigid structure.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43179565","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
Forcing the Σ31-separation property 强制Σ31-separation属性
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-06-22 DOI: 10.1142/s0219061322500088
Stefan Hoffelner
{"title":"Forcing the Σ31-separation property","authors":"Stefan Hoffelner","doi":"10.1142/s0219061322500088","DOIUrl":"https://doi.org/10.1142/s0219061322500088","url":null,"abstract":"We generically construct a model in which the [Formula: see text]-separation property is true, i.e. every pair of disjoint [Formula: see text]-sets can be separated by a [Formula: see text]-definable set. This answers an old question from the problem list “Surrealist landscape with figures” by A. Mathias from 1968. We also construct a model in which the (lightface) [Formula: see text]-separation property is true.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78558140","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
Strong compactness and the ultrapower axiom I: the least strongly compact cardinal 强紧性与超幂公理1:最小强紧基数
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-06-22 DOI: 10.1142/s0219061322500052
G. Goldberg
{"title":"Strong compactness and the ultrapower axiom I: the least strongly compact cardinal","authors":"G. Goldberg","doi":"10.1142/s0219061322500052","DOIUrl":"https://doi.org/10.1142/s0219061322500052","url":null,"abstract":"The Ultrapower Axiom is a combinatorial principle concerning the structure of large cardinals that is true in all known canonical inner models of set theory. A longstanding test question for inner model theory is the equiconsistency of strongly compact and supercompact cardinals. In this paper, it is shown that under the Ultrapower Axiom, the least strongly compact cardinal is supercompact. A number of stronger results are established, setting the stage for a complete analysis of strong compactness and supercompactness under UA that will be carried out in the sequel to this paper.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84381353","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
Every Δ20 degree is a strong degree of categoricity 每一个Δ20度都是一个很强的分类度
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-06-17 DOI: 10.1142/s0219061322500222
Barbara F. Csima, K. Ng
{"title":"Every Δ20 degree is a strong degree of categoricity","authors":"Barbara F. Csima, K. Ng","doi":"10.1142/s0219061322500222","DOIUrl":"https://doi.org/10.1142/s0219061322500222","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83566442","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
Decomposing Aronszajn lines 分解Aronszajn线
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-06-17 DOI: 10.1142/s0219061322500179
Keegan Dasilva Barbosa
{"title":"Decomposing Aronszajn lines","authors":"Keegan Dasilva Barbosa","doi":"10.1142/s0219061322500179","DOIUrl":"https://doi.org/10.1142/s0219061322500179","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90081332","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
Logical Metatheorems for Accretive and (Generalized) Monotone Set-Valued Operators 累加和(广义)单调集值算子的逻辑元定理
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2022-05-03 DOI: 10.1142/s0219061323500083
Nicholas Pischke
{"title":"Logical Metatheorems for Accretive and (Generalized) Monotone Set-Valued Operators","authors":"Nicholas Pischke","doi":"10.1142/s0219061323500083","DOIUrl":"https://doi.org/10.1142/s0219061323500083","url":null,"abstract":"Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain large classes of operators, namely accretive and (generalized) monotone set-valued ones. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie `non-computational' proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46950370","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: 10
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