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This volume contains selected papers from the DIMACS Workshop on Logic and Random Structures held November 5-7, 1995. The workshop was a major event of the DIMACS Special Year on Logic and Algorithms. The central theme was the relationship between logic and probabilistic techniques in the study of finite structures.
In the last several years, this subject has developed into a very active area of mathematical logic with important connections to computer science. The DIMACS workshop was the first of its kind devoted to logic and random structures. Recent work of leaders in the field is contained in the volume, as well as new theoretical developments and applications to computer science.
Foreword ix Preface xi Near model completeness and 0-1 laws John T. Baldwin 1 Smoothness laws for random ordered graphs Ravi B. Boppana and Joel Spencer 15 Spectrally determined first-order limit laws Stanley Burris 33 The asymptotic behavior of Lkinfinity, omega on sparse random graphs Monica McArthur 53 k-universal finite graphs Eric Rosen, Saharon Shelah and Scott Weinstein 65 Monadic second order probabilities in algebra. Directly representable varieties and groups Pawel M. Idziak and Jerzy Tyszkiewicz 79 Approximating the structures accepted by a constant depth circuit or satisfying a sentence--a nonstandard approach Alan R. Woods 109