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The study of random graphs was begun by Paul Erdos and Alfred Renyi in the 1960s and now has a comprehensive literature. A compelling element has been the threshold function, a short range in which events rapidly move from almost certainly false to almost certainly true. This book now joins the study of random graphs (and other random discrete objects) with mathematical logic. The possible threshold phenomena are studied for all statements expressible in a given language. Often there is a zero-one law, that every statement holds with probability near zero or near one. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures. The book will be of interest to graduate students and researchers in discrete mathematics.

Discrete mathematics --- Random graphs --- Logic, Symbolic and mathematical --- Graphes aléatoires --- Logique symbolique et mathématique --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical. --- Random graphs. --- Graphes aléatoires --- Logique symbolique et mathématique --- Graphes, Théorie des. --- Graphes aléatoires. --- Graph theory --- Discrete mathematics. --- Combinatorics. --- Computers. --- Computer science—Mathematics. --- Discrete Mathematics. --- Theory of Computation. --- Mathematics of Computing. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Combinatorics --- Algebra --- Mathematical analysis --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Graphes, Théorie des --- Graph theory. --- Logique mathematique --- Logique du premier ordre

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Mathematics --- 51 --- Math --- Science --- Mathematics. --- 51 Mathematics

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Asymptotic expansions --- Combinatorial analysis --- Combinatorial enumeration problems --- Ramsey numbers --- Asymptotic theory