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Journal of Mathematical Logic最新文献

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Games with filters I 带有过滤器的游戏1
1区 数学
Journal of Mathematical Logic Pub Date : 2023-08-29 DOI: 10.1142/s021906132450003x
Matthew Foreman, Menachem Magidor, Martin Zeman
{"title":"Games with filters I","authors":"Matthew Foreman, Menachem Magidor, Martin Zeman","doi":"10.1142/s021906132450003x","DOIUrl":"https://doi.org/10.1142/s021906132450003x","url":null,"abstract":"This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call Welch games. Player II having a winning strategy in the Welch game of length [Formula: see text] on [Formula: see text] is equivalent to weak compactness. Winning the game of length [Formula: see text] is equivalent to [Formula: see text] being measurable. We show that for games of intermediate length [Formula: see text], II winning implies the existence of precipitous ideals with [Formula: see text]-closed, [Formula: see text]-dense trees. The second part shows the first is not vacuous. For each [Formula: see text] between [Formula: see text] and [Formula: see text], it gives a model where II wins the games of length [Formula: see text], but not [Formula: see text]. The technique also gives models where for all [Formula: see text] there are [Formula: see text]-complete, normal, [Formula: see text]-distributive ideals having dense sets that are [Formula: see text]-closed, but not [Formula: see text]-closed.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136244251","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
Halin's Infinite Ray Theorems: Complexity and Reverse Mathematics 哈林无限射线定理：复杂性与反向数学
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-08-28 DOI: 10.1142/s0219061324500107
James S. Barnes, Jun Le Goh, R. Shore
{"title":"Halin's Infinite Ray Theorems: Complexity and Reverse Mathematics","authors":"James S. Barnes, Jun Le Goh, R. Shore","doi":"10.1142/s0219061324500107","DOIUrl":"https://doi.org/10.1142/s0219061324500107","url":null,"abstract":"Halin [1965] proved that if a graph has $n$ many pairwise disjoint rays for each $n$ then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity. The statement of Halin's theorem and the construction proving it seem very much like standard versions of compactness arguments such as K\"{o}nig's Lemma. Those results, while not computable, are relatively simple. They only use arithmetic procedures or, equivalently, finitely many iterations of the Turing jump. We show that several Halin type theorems are much more complicated. They are among the theorems of hyperarithmetic analysis. Such theorems imply the ability to iterate the Turing jump along any computable well ordering. Several important logical principles in this class have been extensively studied beginning with work of Kreisel, H. Friedman, Steel and others in the 1960s and 1970s. Until now, only one purely mathematical example was known. Our work provides many more and so answers Question 30 of Montalb'{a}n's Open Questions in Reverse Mathematics [2011]. Some of these theorems including ones in Halin [1965] are also shown to have unusual proof theoretic strength as well.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"22 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139348680","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
Maω1 (S)[S] does not imply 𝒦2 Maω1（S）[S]并不意味着𝒦2.
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-07-14 DOI: 10.1142/s0219061324500041
Yinhe Peng, Liuzhen Wu
{"title":"Maω1 (S)[S] does not imply 𝒦2","authors":"Yinhe Peng, Liuzhen Wu","doi":"10.1142/s0219061324500041","DOIUrl":"https://doi.org/10.1142/s0219061324500041","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44519381","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
Hensel minimality: geometric criteria for ℓ-H-minimality Hensel极小性：ℓ-H-极小性
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-07-07 DOI: 10.1142/s0219061324500016
F. Vermeulen
{"title":"Hensel minimality: geometric criteria for ℓ-H-minimality","authors":"F. Vermeulen","doi":"10.1142/s0219061324500016","DOIUrl":"https://doi.org/10.1142/s0219061324500016","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44388121","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
Henselian expansions of nip fields nip域的Henselian扩展
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-03-24 DOI: 10.1142/s021906132350006x
Franziska Jahnke
{"title":"Henselian expansions of nip fields","authors":"Franziska Jahnke","doi":"10.1142/s021906132350006x","DOIUrl":"https://doi.org/10.1142/s021906132350006x","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47928114","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
Corrigendum to Reducing ω-model reflection to iterated syntactic reflection 将ω-模型反射简化为迭代句法反射的勘误表
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-03-06 DOI: 10.1142/s0219061323920010
F. Pakhomov, J. Walsh
{"title":"Corrigendum to Reducing ω-model reflection to iterated syntactic reflection","authors":"F. Pakhomov, J. Walsh","doi":"10.1142/s0219061323920010","DOIUrl":"https://doi.org/10.1142/s0219061323920010","url":null,"abstract":"We fix a gap in a proof in our paper Reducing[Formula: see text]-model reflection to iterated syntactic reflection.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"49 1","pages":"2392001:1-2392001:11"},"PeriodicalIF":0.9,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72540885","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
Exactly two and exactly three near-coherence classes 正好是两个，正好是三个近似连贯类
IF 0.9 1区 数学
Journal of Mathematical Logic Pub Date : 2023-02-10 DOI: 10.1142/s0219061323500034
H. Mildenberger
{"title":"Exactly two and exactly three near-coherence classes","authors":"H. Mildenberger","doi":"10.1142/s0219061323500034","DOIUrl":"https://doi.org/10.1142/s0219061323500034","url":null,"abstract":"","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45919886","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
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":" ","pages":""},"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":"26 1","pages":"2250031:1-2250031:6"},"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":"14 1","pages":"2250029:1-2250029:31"},"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
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