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The Strange Logic of Random Graphs

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概要 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 ev...ents 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.続きを見る
目次 I. Beginnings
0. Two Starting Examples
1. Preliminaries
2. The Ehrenfeucht Game
II. Random Graphs
3. Very Sparse Graphs
4. The Combinatorics of Rooted Graphs
5. The Janson Inequality
6. The Main Theorem
7. Countable Models
8. Near Rational Powers of n
III. Extras
9. A Dynamic View
10. Strings
11. Stronger Logics
12. Three Final Examples.
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登録日 2020.06.27
更新日 2020.06.28