## The Strange Logic of Random GraphsThe study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures. |

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### Contents

The Ehrenfeucht Game | 23 |

3 | 49 |

The Combinatorics of Rooted Graphs 69 | 68 |

The Janson Inequality | 79 |

The Main Theorem | 87 |

Near Rational Powers of n | 103 |

9 | 121 |

Three Final Examples | 153 |

164 | |

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### Common terms and phrases

adjacent Alice's Restaurant asymptotically BIGGAP binary relation Claim cli(x cli(x,a clu(x common neighbor components consider copy of H countable models cycles d-neighborhoods d-picture defined denote dense disjoint Duplicator wins edges Ehrenfeucht Game Ehrenfeucht value EHRV[k elementarily equivalent equivalence class exist expected number finite graph finite number finite set fixed give graph G graph isomorphism hence holds almost surely induction infinite initial segment integers irrational isomorphic k-cycle k-move k-similar limiting probability Ln(H look-ahead marked vertices move nailextension nonroots order language order sentence order theory ordered graph pairs Poisson Poisson distribution positive integer Pr[A precisely probability space Proof quantifier depth random graph Restaurant property result rigid extension rooted graph rooted tree safe extension satisfies the Zero-One schema second order Section semigroup sequence sparse Spoiler selects strategy subextension subgraph substring Suppose sure theory t-closure t-generic Theorem threshold function triangle truth value type v,e unary predicate vertex zero Zero-One Law