{"title":"Kenneth Kunen, Set Theory, Studies in Logic: Mathematical Logic and Foundations, Vol. 34, College Publications, London, 2011, viii + 401 pp","authors":"D. Milovich","doi":"10.1017/BSL.2016.18","DOIUrl":"https://doi.org/10.1017/BSL.2016.18","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83411734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Valerio Capraro and Martino Lupini, Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture, Lecture Notes in Mathematics, vol. 2136, Springer International Publishing, Switzerland, 2015, viii + 151 pp","authors":"L. Bowen","doi":"10.1017/BSL.2016.21","DOIUrl":"https://doi.org/10.1017/BSL.2016.21","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78126547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vladimir Kanovei, Marcin Sabok, and Jindřich Zapletal, Canonical Ramsey Theory on Polish Spaces, Cambridge Tracts in Mathematics, vol. 202, Cambridge University Press, Cambridge, 2013, viii + 269 pp","authors":"Clinton T. Conley","doi":"10.1017/BSL.2016.25","DOIUrl":"https://doi.org/10.1017/BSL.2016.25","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75426958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.
{"title":"Relativizing Operational Set Theory","authors":"Gerhard Jäger","doi":"10.1017/BSL.2016.11","DOIUrl":"https://doi.org/10.1017/BSL.2016.11","url":null,"abstract":"We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/BSL.2016.11","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72452190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"In Memoriam: Barry Cooper 1943-2015","authors":"Andrew Lewis-Pye, A. Sorbi","doi":"10.1017/BSL.2016.17","DOIUrl":"https://doi.org/10.1017/BSL.2016.17","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83964201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear Time in Hypersequent Framework","authors":"Andrzej Indrzejczak","doi":"10.1017/BSL.2016.2","DOIUrl":"https://doi.org/10.1017/BSL.2016.2","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87838077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Obituary: Jaakko Hintikka 1929-2015","authors":"J. Väänänen","doi":"10.1017/BSL.2015.35","DOIUrl":"https://doi.org/10.1017/BSL.2015.35","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73776703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory.
本文从Borel复杂性理论的角度综述了C*-代数自同构分类问题的最新研究进展。
{"title":"The Classification Problem for automorphisms of C*-Algebras","authors":"M. Lupini","doi":"10.1017/BSL.2015.37","DOIUrl":"https://doi.org/10.1017/BSL.2015.37","url":null,"abstract":"We present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73368984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than ML (ML) randomness. We establish several equivalences. Given a ML-random real $z$, the additional randomness strengths needed for the following are equivalent. n (1) all effectively closed classes containing $z$ have density $1$ at $z$. n (2) all nondecreasing functions with uniformly left-c.e. increments are differentiable at $z$. n (3) $z$ is a Lebesgue point of each lower semicomputable integrable function. We also consider convergence of left-c.e. martingales, and convergence in the sense of Birkhoff's pointwise ergodic theorem. Lastly we study randomness notions for density of $Pi^0_n$ and $Sigma^1_1$ classes.
{"title":"Using Almost-everywhere theorems from Analysis to Study Randomness","authors":"Kenshi Miyabe, A. Nies, Jing Zhang","doi":"10.1017/BSL.2016.10","DOIUrl":"https://doi.org/10.1017/BSL.2016.10","url":null,"abstract":"We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than ML (ML) randomness. We establish several equivalences. Given a ML-random real $z$, the additional randomness strengths needed for the following are equivalent. \u0000n (1) all effectively closed classes containing $z$ have density $1$ at $z$. \u0000n (2) all nondecreasing functions with uniformly left-c.e. increments are differentiable at $z$. \u0000n (3) $z$ is a Lebesgue point of each lower semicomputable integrable function. \u0000We also consider convergence of left-c.e. martingales, and convergence in the sense of Birkhoff's pointwise ergodic theorem. Lastly we study randomness notions for density of $Pi^0_n$ and $Sigma^1_1$ classes.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2014-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85489922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.
{"title":"Explicit Mathematics and Operational Set Theory: some Ontological comparisons","authors":"Gerhard Jäger, Rico Zumbrunnen","doi":"10.1017/BSL.2014.21","DOIUrl":"https://doi.org/10.1017/BSL.2014.21","url":null,"abstract":"We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75355604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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