{"title":"Groups of small Morley rank","authors":"G. Cherlin","doi":"10.1016/0003-4843(79)90019-6","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90019-6","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"16 1","pages":"1-28"},"PeriodicalIF":0.0,"publicationDate":"1979-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87304287","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":"Researches into the world of k → (k)k","authors":"J.M. 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":"17 1","pages":"Pages 151-169"},"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)90024-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90016085","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":"Groups of small Morley rank","authors":"Gregory Cherlin","doi":"10.1016/0003-4843(79)90019-6","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90019-6","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 1","pages":"Pages 1-28"},"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)90019-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91682635","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":"Universal equational theories and varieties of algebras","authors":"D. Pigozzi","doi":"10.1016/0003-4843(79)90023-8","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90023-8","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"6 1","pages":"117-150"},"PeriodicalIF":0.0,"publicationDate":"1979-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90678461","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":"Universal equational theories and varieties of algebras","authors":"Don Pigozzi","doi":"10.1016/0003-4843(79)90023-8","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90023-8","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 1","pages":"Pages 117-150"},"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)90023-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90016086","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":"A computable ordinary differential equation which possesses no computable solution","authors":"Marian Boylan Pour-el, I. Richards","doi":"10.1016/0003-4843(79)90021-4","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90021-4","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"54 1","pages":"61-90"},"PeriodicalIF":0.0,"publicationDate":"1979-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77956916","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":"A computable ordinary differential equation which possesses no computable solution","authors":"Marian Boylan Pour-el, Ian Richards","doi":"10.1016/0003-4843(79)90021-4","DOIUrl":"https://doi.org/10.1016/0003-4843(79)90021-4","url":null,"abstract":"<div><p>We prove that there exists a computable—and hence continuous,-function <em>F</em>(v,x) defined α a rectangle <em>R</em> of the plane such that the differential equation <em>x</em>′=<em>F</em><sub><em>x</em>,<em>v</em></sub> has no computable solution of any neighborhood within <em>R</em>. As an immediate corollary, we obtain from the form of the above differential equation a computable transformation with no computable fixed point.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"17 1","pages":"Pages 61-90"},"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)90021-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91682634","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":"Isomorphism and higher order equivalence","authors":"M. Ajtai","doi":"10.1016/0003-4843(79)90001-9","DOIUrl":"10.1016/0003-4843(79)90001-9","url":null,"abstract":"","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"16 3","pages":"Pages 181-203"},"PeriodicalIF":0.0,"publicationDate":"1979-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(79)90001-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88509077","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":"On α- and β-recursively enumerable degrees","authors":"Wolfgang Maass","doi":"10.1016/0003-4843(79)90002-0","DOIUrl":"10.1016/0003-4843(79)90002-0","url":null,"abstract":"<div><p>Several problems in recursion theory on admissible ordinals (α-recursion theory) and recursion theory of inadmissible ordinals (β-recursion theory) are studied. Fruitful interactions between both theories are stressed. In the first part of the admissible collapse is used in order to characterize for some inadmissible β the structure of all β-recursively enumerable degrees as an accumulation of structures of <span><math><mtext>U</mtext></math></span>-recursively enumerable degrees for many admissible structures <span><math><mtext>U</mtext></math></span>. Thus problems about the β-recursively enumerable degrees can be solved by considering “locally” the analogous problem in an admissible <span><math><mtext>U</mtext></math></span> (where results of α-recursion theory apply). In the second part β-recursion theory is used as a tool in infinite injury priority constructions for some particularly interesting α (e.g. <em>ω</em><sub>1</sub><sup>CK</sup>). New effects can be observed since some structure of the inadmissible world above <em>O</em>′ is projected into the α-recursively enumerable degrees by inverting the jump. The gained understanding of the jump of α-recursively enumerable degrees makes it possible to solve some open problems.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"16 3","pages":"Pages 205-231"},"PeriodicalIF":0.0,"publicationDate":"1979-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(79)90002-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91518467","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}