Pub Date : 1980-11-01DOI: 10.1016/0003-4843(80)90020-0
Alan Adamson
{"title":"Saturated structures, unions of chains, and preservation theorems","authors":"Alan Adamson","doi":"10.1016/0003-4843(80)90020-0","DOIUrl":"10.1016/0003-4843(80)90020-0","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"19 1","pages":"Pages 67-96"},"PeriodicalIF":0.0,"publicationDate":"1980-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90020-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87759624","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}
Pub Date : 1980-08-01DOI: 10.1016/0003-4843(80)90006-6
G. Cherlin , S. Shelah
We prove an indecomposability theorem for connected stable groups. Using this theorem we prove that all infinite superstable fields are algebraically closed, and we extend known results for ω-stable groups of Morley rank at most 3 to the corresponding class of superstable groups (Note: The logical notion of stability is unrelated to the notion of stability in finit group theory).
{"title":"Superstable fields and groups","authors":"G. Cherlin , S. Shelah","doi":"10.1016/0003-4843(80)90006-6","DOIUrl":"10.1016/0003-4843(80)90006-6","url":null,"abstract":"<div><p>We prove an indecomposability theorem for connected stable groups. Using this theorem we prove that all infinite superstable fields are algebraically closed, and we extend known results for ω-stable groups of Morley rank at most 3 to the corresponding class of superstable groups (Note: The logical notion of stability is unrelated to the notion of stability in finit group theory).</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 3","pages":"Pages 227-270"},"PeriodicalIF":0.0,"publicationDate":"1980-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90006-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82688701","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}
Pub Date : 1980-08-01DOI: 10.1016/0003-4843(80)90005-4
Jouko Väänänen
A theory of Boolean valued models for generalize quantifiers is developed with a special emphasis on the Härtig-quantifier. As an application a Boolean extension is obtained in which the decision problem of the Härtig-quantifier is .
{"title":"Boolean valued models and generalized quantifiers","authors":"Jouko Väänänen","doi":"10.1016/0003-4843(80)90005-4","DOIUrl":"10.1016/0003-4843(80)90005-4","url":null,"abstract":"<div><p>A theory of Boolean valued models for generalize quantifiers is developed with a special emphasis on the Härtig-quantifier. As an application a Boolean extension is obtained in which the decision problem of the Härtig-quantifier is <span><math><mtext>Δ</mtext><mtext>1</mtext><mtext>2</mtext></math></span>.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 3","pages":"Pages 193-225"},"PeriodicalIF":0.0,"publicationDate":"1980-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90005-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82993509","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}
Pub Date : 1980-06-01DOI: 10.1016/0003-4843(80)90016-9
J.B. Remmel
{"title":"Recursion theory on algebraic structures with independent sets","authors":"J.B. Remmel","doi":"10.1016/0003-4843(80)90016-9","DOIUrl":"10.1016/0003-4843(80)90016-9","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 2","pages":"Pages 153-191"},"PeriodicalIF":0.0,"publicationDate":"1980-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90016-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83234268","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}
Pub Date : 1980-06-01DOI: 10.1016/0003-4843(80)90014-5
James F. Lynch
If is a model with universe where q is a fixed positive integer, we put 〈Q〉 for the expansion of with the new relation Q. We study sets of relations defined by where σ is a first-order sentence with equality of the appropriate type and . For some simple countable structures , we show that S(σ) is almost all of 2 or almost none of it, for certain topologies and measures. We have analogous results for the cardinality of S(σ) for some finite structures with large enough U.
Some of the structures we examine, in both the countable and finite case, are sets with a successor relation and cyclic groups.
{"title":"Almost sure theories","authors":"James F. Lynch","doi":"10.1016/0003-4843(80)90014-5","DOIUrl":"10.1016/0003-4843(80)90014-5","url":null,"abstract":"<div><p>If <figure><img></figure> is a model with universe <span><math><mtext>U </mtext><mtext>and</mtext><mtext> Q ⊆ </mtext><msup><mi></mi><mn>q</mn></msup><mtext>U</mtext></math></span> where q is a fixed positive integer, we put <figure><img></figure>〈<em>Q</em>〉 for the expansion of <figure><img></figure> with the new relation <em>Q</em>. We study sets of relations defined by <span><span><span><math><mtext>S(σ) = {Q⊆</mtext><msup><mi></mi><mn>q</mn></msup><mtext>U:</mtext><mglyph></mglyph><mtext>〈Q〉⊨σ}</mtext></math></span></span></span> where σ is a first-order sentence with equality of the appropriate type and <span><math><mtext>|U|⩽ℵ</mtext><msub><mi></mi><mn>0</mn></msub></math></span>. For some simple countable structures <figure><img></figure>, we show that <em>S</em>(<em>σ</em>) is almost all of <figure><img></figure>2 or almost none of it, for certain topologies and measures. We have analogous results for the cardinality of <em>S</em>(<em>σ</em>) for some finite structures <figure><img></figure> with large enough <em>U</em>.</p><p>Some of the structures we examine, in both the countable and finite case, are sets with a successor relation and cyclic groups.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 2","pages":"Pages 91-135"},"PeriodicalIF":0.0,"publicationDate":"1980-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90014-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77078501","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}
Pub Date : 1980-03-01DOI: 10.1016/0003-4843(80)90004-2
Anil Nerode, Richard A. Shore
{"title":"Reducibility orderings: Theories, definability and automorphisms","authors":"Anil Nerode, Richard A. Shore","doi":"10.1016/0003-4843(80)90004-2","DOIUrl":"10.1016/0003-4843(80)90004-2","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 1","pages":"Pages 61-89"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90004-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90855176","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}
Pub Date : 1980-03-01DOI: 10.1016/0003-4843(80)90003-0
Jacques Stern
{"title":"Effective partitions of the real line into Borel sets of bounded rank","authors":"Jacques Stern","doi":"10.1016/0003-4843(80)90003-0","DOIUrl":"10.1016/0003-4843(80)90003-0","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 1","pages":"Pages 29-60"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90003-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87271062","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}
Pub Date : 1980-03-01DOI: 10.1016/0003-4843(80)90002-9
Jack H. Silver
{"title":"Counting the number of equivalence classes of Borel and coanalytic equivalence relations","authors":"Jack H. Silver","doi":"10.1016/0003-4843(80)90002-9","DOIUrl":"10.1016/0003-4843(80)90002-9","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"18 1","pages":"Pages 1-28"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(80)90002-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82177498","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}
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