Two Starting Examples
The core of our work is the study of Zero-One Laws for sparse random graphs. We may think of this study as having two sources. The first is the Zero-One Law for random graphs with constant probability, as given in Section 0.1. The second is the notion of evolution of random graph as discussed in Section 1.1.1. In that evolution it is central that the edge probability p be taken not just as a constant but as a function p = p(n) of the total number of vertices. In Section 0.2 we examine such an evolution in the much easier case of a random unary predicate. To allow an easy introduction we avoid a plethora of notation in this chapter, the technical preliminaries — including many key definitions — are left for Chapter 1 and beyond.
KeywordsRandom Graph Threshold Function Countable Model Unary Predicate Infinite Graph
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