{"title":"Effective content of field theory","authors":"G. Metakides, A. Nerode","doi":"10.1016/0003-4843(79)90011-1","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90011-1","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"31 1","pages":"289-320"},"PeriodicalIF":0.0,"publicationDate":"1979-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79152040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stationary logic of finitely determinate structures","authors":"Paul C. Eklof , Alan H. Mekler","doi":"10.1016/0003-4843(79)90009-3","DOIUrl":"10.1016/0003-4843(79)90009-3","url":null,"abstract":"<div><p>In this part we develop the theory of finitely determinate structures, that is, structures on which the dual quantifiers “stat” and “unreadable” have the same meaning. Among other general</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 3","pages":"Pages 227-269"},"PeriodicalIF":0.0,"publicationDate":"1979-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(79)90009-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89241009","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 content of field theory","authors":"G. Metakides, A. Nerode","doi":"10.1016/0003-4843(79)90011-1","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90011-1","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 3","pages":"Pages 289-320"},"PeriodicalIF":0.0,"publicationDate":"1979-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(79)90011-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72276236","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":"Model-complete theories of pseudo-algebraically closed fields","authors":"William H. Wheeler","doi":"10.1016/0003-4843(79)90008-1","DOIUrl":"10.1016/0003-4843(79)90008-1","url":null,"abstract":"<div><p>The model-complete, complete theories of pseudo-algebraically closed fields are characterized in this paper. For example, the theory of algebraically closed fields of a specified characteristic is a model-complete, complete theory of pseudo-algebraically closed fields. The characterization is based upon the algebraic properties of the theories' associated number fields and is the first step towards a classification of all the model-complete, complete theories of fields.</p><p>A field <em>F</em> is<em>pseudo-algebraically closed</em> if whenever <em>I</em> is a prime ideal in a polynomial ring <em>F[x<sub>1</sub>...x<sub>m</sub>]=F[x]</em> and <em>F</em> is algebraically closed in the quotient field of <em>F[x]/l</em>, then there is a homorphism from <em>F[x]/l</em> into <em>F</em> which is the identity on <em>F</em>. The field <em>F</em> can be pseudo-algebraically closed but <em>not perfect</em>; indeed, the non-perfect case is one of the interesting aspects of this paper. Heretofore, this concept has been considered only for a perfect field <em>F</em>, in which case it is equivalent to each nonvoid, absolutely irreducible <em>F</em>-variety's having an <em>F</em>-rational point. The perfect, pseudo-algebraically closed fields have been prominent in recent metamathematical investigations of fields [1, 2, 3, 11, 12, 13, 14, 15, 28]. Reference [14] in particular is the algebraic springboard for this paper.</p><p>A field <em>F</em> has <em>bounded corank</em> if <em>F</em> has only finitely many separable algebraic extensions of degree <em>n</em> over <em>F</em> for each integer <em>n</em>⩾2.</p><p>A field <em>F</em> will be called an <em>B</em>-field for an integral domain <em>B</em> if <em>B</em> is a sabring of <em>F</em>.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 3","pages":"Pages 205-226"},"PeriodicalIF":0.0,"publicationDate":"1979-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(79)90008-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77742275","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":"Progress report on generalized functionality","authors":"Jonathan P. Seldin","doi":"10.1016/0003-4843(79)90020-2","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90020-2","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 1","pages":"Pages 29-59"},"PeriodicalIF":0.0,"publicationDate":"1979-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(79)90020-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91726302","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":"Researches into the world of k → (k)k","authors":"J. Henle","doi":"10.1016/0003-4843(79)90024-X","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90024-X","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"3 1","pages":"151-169"},"PeriodicalIF":0.0,"publicationDate":"1979-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89641996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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