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Annals of Mathematical Logic最新文献

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Recursive models for constructive set theories 构造集理论的递归模型
Annals of Mathematical Logic Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90003-1
M. Beeson
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引用次数: 45
Morasses, diamond, and forcing 沼泽，钻石，强迫
Annals of Mathematical Logic Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90005-5
Daniel J. Velleman
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引用次数: 48
A very absolute Π21 real singleton 一个非常绝对的Π21真正的单身
Annals of Mathematical Logic Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90001-8
René David
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引用次数: 16
Δ31 reals Δ31个实数
Annals of Mathematical Logic Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90002-X
René David
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引用次数: 1
Monadic theory of order and topology in ZFC ZFC中单元序和拓扑理论
Annals of Mathematical Logic Pub Date : 1982-12-01 DOI: 10.1016/0003-4843(82)90004-3
Yuri Gurevich, Saharon Shelah
{"title":"Monadic theory of order and topology in ZFC","authors":"Yuri Gurevich,&nbsp;Saharon Shelah","doi":"10.1016/0003-4843(82)90004-3","DOIUrl":"https://doi.org/10.1016/0003-4843(82)90004-3","url":null,"abstract":"<div><p>True first-order arithmetic is interpreted in the monadic theories of certain chains and topological spaces including the real line and the Cantor Discontinuum. It was known that existence of such interpretations in consistent with ZFC.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"23 2","pages":"Pages 179-198"},"PeriodicalIF":0.0,"publicationDate":"1982-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(82)90004-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"109185674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 41
Concepts of general topology in constructive mathematics and in sheaves, II 构造数学中一般拓扑学的概念，2
Annals of Mathematical Logic Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90010-9
R.J. Grayson
{"title":"Concepts of general topology in constructive mathematics and in sheaves, II","authors":"R.J. Grayson","doi":"10.1016/0003-4843(82)90010-9","DOIUrl":"10.1016/0003-4843(82)90010-9","url":null,"abstract":"<div><p>Topological properties of spaces of sections of bundles are investigated in detail, and connected with results in constructive topology, in particular for notions of compactness, connectedness and uniformity.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"23 1","pages":"Pages 55-98"},"PeriodicalIF":0.0,"publicationDate":"1982-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(82)90010-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127623066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
The Boolean algebra of formulas of first-order logic 一阶逻辑公式的布尔代数
Annals of Mathematical Logic Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90009-2
Don H. Faust
{"title":"The Boolean algebra of formulas of first-order logic","authors":"Don H. Faust","doi":"10.1016/0003-4843(82)90009-2","DOIUrl":"10.1016/0003-4843(82)90009-2","url":null,"abstract":"<div><p>The algebraic and recursive structure of countable languages of classical first-order logic with equality is analysed. All languages of finite undecidable similarity type are shown to be algebraically and recursively equivalent in the following sense: their Boolean algebras of formulas are, after trivial involving the one element models of the languages have been excepted, recursively isomorphic by a map which preserves the degree of recursiveness of their models.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"23 1","pages":"Pages 27-53"},"PeriodicalIF":0.0,"publicationDate":"1982-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(82)90009-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126173594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Decidability and stability of free nilpotent lie algebras and free nilpotent p-groups of finite exponent 自由幂零李代数和有限指数的自由幂零p群的可决性和稳定性
Annals of Mathematical Logic Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90008-0
Andreas Baudisch
{"title":"Decidability and stability of free nilpotent lie algebras and free nilpotent p-groups of finite exponent","authors":"Andreas Baudisch","doi":"10.1016/0003-4843(82)90008-0","DOIUrl":"10.1016/0003-4843(82)90008-0","url":null,"abstract":"<div><p>Our main result is the decidability and ω-stability of free <em>c</em>th nilpotent <em>p</em>-groups of finite exponent (<em>c</em> &lt; <em>p</em>).</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"23 1","pages":"Pages 1-25"},"PeriodicalIF":0.0,"publicationDate":"1982-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(82)90008-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121719240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
A correction to “concepts of general topology in constructive mathematics and in sheaves” 对“构造数学中的一般拓扑学概念和束”的修正
Annals of Mathematical Logic Pub Date : 1982-10-01 DOI: 10.1016/0003-4843(82)90011-0
R.J. Grayson
{"title":"A correction to “concepts of general topology in constructive mathematics and in sheaves”","authors":"R.J. Grayson","doi":"10.1016/0003-4843(82)90011-0","DOIUrl":"10.1016/0003-4843(82)90011-0","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"23 1","pages":"Page 99"},"PeriodicalIF":0.0,"publicationDate":"1982-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(82)90011-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121670689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the completenes principle: A study of provability in heyting's arithmetic and extensions 完备原理:heyting算法及其扩展的可证明性研究
Annals of Mathematical Logic Pub Date : 1982-08-01 DOI: 10.1016/0003-4843(82)90024-9
Albert Visser
{"title":"On the completenes principle: A study of provability in heyting's arithmetic and extensions","authors":"Albert Visser","doi":"10.1016/0003-4843(82)90024-9","DOIUrl":"10.1016/0003-4843(82)90024-9","url":null,"abstract":"<div><p>In this paper extensions of HA are studied that prove their own completeness, i.e. they prove <em>A</em> → □ <em>A</em>, where □ is interpreted as provability in the theory itself. Motivation is three-fold: (1) these theories are thought to have some intrinsic interest, (2) they are a tool for producing and studying provability principles, (3) they can be used to proved independence results. Work done in the paper connected with these motivations is respectively: </p><ul><li><span>1.</span><span><p>(i) A characterization is given of theories proving their own completeness, including an appropriate conservation result.</p></span></li><li><span>2.</span><span><p>(ii) Some new provability principles are produced. The provability logic of HA is not a sublogic of the of PA. A provability logic plus completeness theorem is given for a certain intuitionistic extension of HA. De Jongh's theorem for propositional logic is a corollary.</p></span></li><li><span>3.</span><span><p>(iii) FP-realizability in Beeson's proof that <span><math><mtext>∦</mtext><msub><mi></mi><mn><mtext>HA</mtext></mn></msub></math></span> KLS is replaced by theories proving their own completeness. New consequences are <span><math><mtext>∦</mtext><msub><mi></mi><mn><mtext>HA</mtext><mtext>+−</mtext><mtext>M</mtext><msub><mi></mi><mn>PR</mn></msub></mn></msub><mtext> </mtext><mtext>KLS</mtext></math></span>, <span><math><mtext>∦</mtext><msub><mi></mi><mn><mtext>HA+DNS</mtext></mn></msub><mtext> </mtext><mtext>KLS</mtext></math></span>.</p></span></li></ul></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"22 3","pages":"Pages 263-295"},"PeriodicalIF":0.0,"publicationDate":"1982-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(82)90024-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128488563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 53
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