Pub Date : 2008-12-01DOI: 10.1017/S1079898600001505
P. Hájek
{"title":"Graham Priest. An introduction to non-classical logic: From If to Is . Second Edition. Cambridge University Press, Cambridge, United Kingdom, 2008, xxxii + 613 pp.","authors":"P. Hájek","doi":"10.1017/S1079898600001505","DOIUrl":"https://doi.org/10.1017/S1079898600001505","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"544 - 545"},"PeriodicalIF":0.6,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001505","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303111","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}
s of the invited talks and contributed talks given (in person or by title) by members of the Association for Symbolic Logic follow. For the Program Committee Gila Sher Abstracts of invited papers for the Symposium on Quantifiers in Logic and Languages of invited papers for the Symposium on Quantifiers in Logic and Language CHRIS BARKER, Reasoning about scope-taking in a substructural logic. NYU Linguistics, 726 Broadway, 7th floor, New York, NY 10003, USA. E-mail: Chris. Barker@nyu. edu. ? 2008, Association for Symbolic Logic 1079-8986/08/1403-0007/$1.60
{"title":"2008 Spring Meeting of the Association for Symbolic Logic","authors":"G. Sher","doi":"10.2178/bsl/1231081375","DOIUrl":"https://doi.org/10.2178/bsl/1231081375","url":null,"abstract":"s of the invited talks and contributed talks given (in person or by title) by members of the Association for Symbolic Logic follow. For the Program Committee Gila Sher Abstracts of invited papers for the Symposium on Quantifiers in Logic and Languages of invited papers for the Symposium on Quantifiers in Logic and Language CHRIS BARKER, Reasoning about scope-taking in a substructural logic. NYU Linguistics, 726 Broadway, 7th floor, New York, NY 10003, USA. E-mail: Chris. Barker@nyu. edu. ? 2008, Association for Symbolic Logic 1079-8986/08/1403-0007/$1.60","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"412 - 417"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081375","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346943","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}
of 19 Annual Gödel Lecture W. HUGH WOODIN, The Continuum Hypothesis, the Ω Conjecture, and the inner model problem for one supercompact cardinal. Department of Mathematics, The University of California, 721 Evans Hall #3840, Berkeley, CA 94720-3840 US. E-mail: woodin@math.berkeley.edu. The Ω Conjecture is a key element of an argument that the Continuum Hypothesis is false, based on notions of simplicity. While this application is certainly debatable, there is a much stronger argument that if the Ω Conjecture is true then the Continuum Hypothesis must have an answer. In brief, the Ω Conjecture rules out amultiverse conception of truth in Set Theory which is based on the generic multiverse. The ΩConjecture is invariant under passing from the universe of sets to a generic extension of the universe of sets, and so it is reasonable to expect that if the Ω Conjecture is false then it must be refuted by some large cardinal hypothesis. The search for candidates for such a large cardinal hypothesis leads to the inner model problem since subject to fairly general criteria, if the inner model problem can be solved for a particular large cardinal hypothesis then that large cardinal hypothesis cannot refute the Ω Conjecture. Again subject to fairly general criteria for a successful inner model construction, the entire inner model program can now be reduced to the case of exactly one supercompact cardinal. If this one case can be solved then one obtains an ultimate generalization of Gödel’s, Axiom of Constructibility, and one also obtains that no (known) large cardinal hypothesis can refute the Ω Conjecture. I shall survey how the inner model problem for one supercompact cardinal has emerged as the critical case, the connections with the Ω Conjecture, and the connections to transfinite generalizations of the Axiom of Determinacy. My emphasis will be less on the technical details and more on what I think are the key foundational issues. Abstract of Special Lecture in honor of Paul Eklofof Special Lecture in honor of Paul Eklof SAHARON SHELAH, Incompactness in singular cardinals. Department of Mathematics, Hebrew University, Jerusalem, Israel 91905. E-mail: shelah@math.huji.ac.il. We prove the consistency of: is strong limit singular and for some properties of Abelian 42
19年度Gödel讲座W. HUGH WOODIN，连续介质假设，Ω猜想，以及一个超紧基数的内模问题。加州大学数学系，721 Evans Hall #3840, Berkeley, CA 94720-3840 US。电子邮件:woodin@math.berkeley.edu。Ω猜想是一个论点的关键元素，连续统假设是错误的，基于简单的概念。虽然这个应用当然是有争议的，但有一个更有力的论点，如果Ω猜想是真的，那么连续统假设一定有一个答案。简而言之，Ω猜想排除了基于一般多重宇宙的集合论中的多重宇宙真理概念。ΩConjecture在从集合域过渡到集合域的一般扩展时是不变的，因此我们有理由认为，如果Ω猜想是假的，那么它必须被一些大的基本假设所反驳。寻找这样一个大基数假设的候选者会导致内部模型问题，因为根据相当一般的标准，如果内部模型问题可以为一个特定的大基数假设解决，那么这个大基数假设就不能反驳Ω猜想。再一次服从于一个成功的内部模型构造的相当一般的标准，整个内部模型程序现在可以被简化为一个超紧凑基数的情况。如果这一情况可以解决，那么我们就得到了Gödel的构造性公理的最终推广，并且我们也得到了没有(已知的)大的基本假设可以反驳Ω猜想。我将调查一个超紧基数的内模问题是如何作为临界情况出现的，它与Ω猜想的联系，以及它与确定性公理的超限推广的联系。我的重点将不是技术细节，而是我认为的关键基础问题。纪念保罗·埃克洛夫的特别讲座摘要。纪念保罗·埃克洛夫的特别讲座。萨哈伦·希拉，奇异基数中的不紧性。希伯来大学数学系，以色列耶路撒冷91905。电子邮件:shelah@math.huji.ac.il。证明了:是强极限奇异的一致性，并证明了Abelian 42的一些性质
{"title":"2008 Annual Meeting of the Association for Symbolic Logic","authors":"C. Laskowski","doi":"10.2178/bsl/1231081376","DOIUrl":"https://doi.org/10.2178/bsl/1231081376","url":null,"abstract":"of 19 Annual Gödel Lecture W. HUGH WOODIN, The Continuum Hypothesis, the Ω Conjecture, and the inner model problem for one supercompact cardinal. Department of Mathematics, The University of California, 721 Evans Hall #3840, Berkeley, CA 94720-3840 US. E-mail: woodin@math.berkeley.edu. The Ω Conjecture is a key element of an argument that the Continuum Hypothesis is false, based on notions of simplicity. While this application is certainly debatable, there is a much stronger argument that if the Ω Conjecture is true then the Continuum Hypothesis must have an answer. In brief, the Ω Conjecture rules out amultiverse conception of truth in Set Theory which is based on the generic multiverse. The ΩConjecture is invariant under passing from the universe of sets to a generic extension of the universe of sets, and so it is reasonable to expect that if the Ω Conjecture is false then it must be refuted by some large cardinal hypothesis. The search for candidates for such a large cardinal hypothesis leads to the inner model problem since subject to fairly general criteria, if the inner model problem can be solved for a particular large cardinal hypothesis then that large cardinal hypothesis cannot refute the Ω Conjecture. Again subject to fairly general criteria for a successful inner model construction, the entire inner model program can now be reduced to the case of exactly one supercompact cardinal. If this one case can be solved then one obtains an ultimate generalization of Gödel’s, Axiom of Constructibility, and one also obtains that no (known) large cardinal hypothesis can refute the Ω Conjecture. I shall survey how the inner model problem for one supercompact cardinal has emerged as the critical case, the connections with the Ω Conjecture, and the connections to transfinite generalizations of the Axiom of Determinacy. My emphasis will be less on the technical details and more on what I think are the key foundational issues. Abstract of Special Lecture in honor of Paul Eklofof Special Lecture in honor of Paul Eklof SAHARON SHELAH, Incompactness in singular cardinals. Department of Mathematics, Hebrew University, Jerusalem, Israel 91905. E-mail: shelah@math.huji.ac.il. We prove the consistency of: is strong limit singular and for some properties of Abelian 42","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"418 - 437"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68347033","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}
Abstract Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and—in particular—the effectively-computable functions on string representations of numbers.
{"title":"A Natural Axiomatization of Computability and Proof of Church's Thesis","authors":"N. Dershowitz, Y. Gurevich","doi":"10.2178/bsl/1231081370","DOIUrl":"https://doi.org/10.2178/bsl/1231081370","url":null,"abstract":"Abstract Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and—in particular—the effectively-computable functions on string representations of numbers.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"299 - 350"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081370","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346632","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}
Abstract The well known Wiener-Kuratowski explicit definition of the ordered pair, which sets (x,y) = {{x}, {x,y}}, works well in many set theories but fails for those with classes which cannot be members of singletons. With the aid of the Axiom of Foundation, we propose a recursive definition of ordered pair which addresses this shortcoming and also naturally generalizes to ordered tuples of greater length. There are many advantages to the new definition, for it allows for uniform definitions working equally well in a wide range of models for set theories. In ZFC and closely related theories, the rank of an ordered pair of two infinite sets under the new definition turns out to be equal to the maximum of the ranks of the sets.
{"title":"Reconsidering Ordered Pairs","authors":"D. Scott, D. McCarty","doi":"10.2178/bsl/1231081372","DOIUrl":"https://doi.org/10.2178/bsl/1231081372","url":null,"abstract":"Abstract The well known Wiener-Kuratowski explicit definition of the ordered pair, which sets (x,y) = {{x}, {x,y}}, works well in many set theories but fails for those with classes which cannot be members of singletons. With the aid of the Axiom of Foundation, we propose a recursive definition of ordered pair which addresses this shortcoming and also naturally generalizes to ordered tuples of greater length. There are many advantages to the new definition, for it allows for uniform definitions working equally well in a wide range of models for set theories. In ZFC and closely related theories, the rank of an ordered pair of two infinite sets under the new definition turns out to be equal to the maximum of the ranks of the sets.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"379 - 397"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081372","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346288","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}
Abstract We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.
本文讨论了Paul Cohen在集合论中的工作及其影响，特别是力的背景、发现和发展。
{"title":"Cohen and Set Theory","authors":"A. Kanamori","doi":"10.2178/bsl/1231081371","DOIUrl":"https://doi.org/10.2178/bsl/1231081371","url":null,"abstract":"Abstract We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"351 - 378"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081371","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346206","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：