The Strange Logic of Random Graphs [1 ed.] 3540416544, 9783540416548
The study of random graphs was begun by Paul Erdos and Alfred Renyi in the 1960s and now has a comprehensive literature.
252 69 1MB
English Pages 168 [179] Year 2001
Table of contents :
Front Matter....Pages I-X
Front Matter....Pages 1-1
Two Starting Examples....Pages 3-12
Preliminaries....Pages 13-21
The Ehrenfeucht Game....Pages 23-45
Front Matter....Pages 47-47
Very Sparse Graphs....Pages 49-67
The Combinatorics of Rooted Graphs....Pages 69-77
The Janson Inequality....Pages 79-86
The Main Theorem....Pages 87-91
Countable Models....Pages 93-102
Near Rational Powers of n ....Pages 103-118
Front Matter....Pages 119-119
A Dynamic View....Pages 121-129
Strings....Pages 131-144
Stronger Logics....Pages 145-151
Three Final Examples....Pages 153-163
Back Matter....Pages 165-168
Front Matter....Pages I-X
Front Matter....Pages 1-1
Two Starting Examples....Pages 3-12
Preliminaries....Pages 13-21
The Ehrenfeucht Game....Pages 23-45
Front Matter....Pages 47-47
Very Sparse Graphs....Pages 49-67
The Combinatorics of Rooted Graphs....Pages 69-77
The Janson Inequality....Pages 79-86
The Main Theorem....Pages 87-91
Countable Models....Pages 93-102
Near Rational Powers of n ....Pages 103-118
Front Matter....Pages 119-119
A Dynamic View....Pages 121-129
Strings....Pages 131-144
Stronger Logics....Pages 145-151
Three Final Examples....Pages 153-163
Back Matter....Pages 165-168
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