{"title":"The asymptotic behavior of Lk∞,ω on sparse random graphs","authors":"Monica McArthur","doi":"10.1090/dimacs/033/04","DOIUrl":"https://doi.org/10.1090/dimacs/033/04","url":null,"abstract":"","PeriodicalId":363831,"journal":{"name":"Logic and Random Structures","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115796437","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":"K-universal Finite Graphs","authors":"Eric Rosen, S. Shelah, S. Weinstein","doi":"10.1090/dimacs/033/05","DOIUrl":"https://doi.org/10.1090/dimacs/033/05","url":null,"abstract":"This paper investigates the class of k universal nite graphs a local analog of the class of universal graphs which arises naturally in the study of nite variable logics The main results of the paper which are due to Shelah establish that the class of k universal graphs is not de nable by an in nite disjunction of rst order existential sentences with a nite number of variables and that there exist k universal graphs with no k extendible induced subgraphs","PeriodicalId":363831,"journal":{"name":"Logic and Random Structures","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124008859","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":"Smoothness laws for random ordered graphs","authors":"R. Boppana, J. Spencer","doi":"10.1090/dimacs/033/02","DOIUrl":"https://doi.org/10.1090/dimacs/033/02","url":null,"abstract":"","PeriodicalId":363831,"journal":{"name":"Logic and Random Structures","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130742299","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":"Monadic second order probabilities in algebra. Directly representable varieties and groups","authors":"P. Idziak, Jerzy Tyszkiewicz","doi":"10.1090/dimacs/033/06","DOIUrl":"https://doi.org/10.1090/dimacs/033/06","url":null,"abstract":"We analyze the question of existence of asymptotic cumulative probabilities for monadic second order deenable properties of nite algebras. We focus our attention on the directly representable varieties and on the variety of groups. We prove in a very strong way that some recently proven rst-order 0{1 laws and limit laws for these varieties cannot be extended to monadic second order logic. Namely, if the function (n; A) 7 ! pr n fAg] assigning probabilities to structures is recursive, then the 0{1 law holds according to the sequence fpr n g = pr 1 ; pr 2 ; : : : of probabilities ii asymptotically there exists fpr n g-almost surely precisely one algebra. Similarly, the convergence law holds ii asymptotically there are no large algebras according to fpr n g:","PeriodicalId":363831,"journal":{"name":"Logic and Random Structures","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122755164","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":"Near model completeness and 0-1 laws","authors":"J. Baldwin","doi":"10.1090/dimacs/033/01","DOIUrl":"https://doi.org/10.1090/dimacs/033/01","url":null,"abstract":"We work throughout in a finite relational language L. Our aim is to analyze in as purely a model-theoretic context as possible some recent results of Shelah et al in which 0 − 1-laws for random structures of various types are proved by a specific kind of quantifier elimination: near model completeness. In Section 2 we describe the major results of these methods ([12], [11] etc.) and some of their context. In Section 3 we describe the framework in which these arguments can be carried out and prove one form of the general quantification elimination argument. We conclude the section by sketching a general outline of the proof of a 0−1 law. The hypotheses of this theorem have a ‘back and forth’ character. Establishing the ‘forth’ part depends heavily on probability computations and is not expounded here. The ‘back’ part is purely model theory. Section 4 carries out the ‘back’ portion of the proof in one context with some simplification from Shelah’s original version.","PeriodicalId":363831,"journal":{"name":"Logic and Random Structures","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115995013","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":"Approximating the structures accepted by a constant depth circuit or satisfying a sentence-a nonstandard approach","authors":"Alan R. Woods","doi":"10.1090/dimacs/033/07","DOIUrl":"https://doi.org/10.1090/dimacs/033/07","url":null,"abstract":"","PeriodicalId":363831,"journal":{"name":"Logic and Random Structures","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133519135","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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