{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}