{"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}
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
{"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}
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:
研究了一类单进二阶可灭性的渐近累积概率的存在性问题。我们把注意力集中在直接可表征的品种和群体的多样性上。我们强有力地证明了最近证明的一些关于这些变体的一阶0{1定律和极限定律不能推广到一元二阶逻辑中。即，如果函数(n;A) 7个!pr ng]为结构分配概率是递归的，则根据序列fpr ng = pr 1, 0{1定律成立;Pr 2;在概率ii的情况下，FPR在g中几乎可以精确地存在于一个代数中。同样地，收敛律渐近地证明不存在根据fpr ng的大代数:
{"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}
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.
{"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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