The 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.
Table of ContentsI. 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.