The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous n-tournaments (Memoirs of the American Mathematical Society)

The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous n-tournaments (Memoirs of the American Mathematical Society)

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Description

In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use. It features: interface between combinatorics and model theory; unusual use of Ramsey's theorem to classify structures; an extension of an already elaborate branch of model theory; and the first monograph on Lachlan's method.

Contents

Results and open problems Homogeneous $2$-tournaments Homogeneous $n$-tournaments Homogeneous symmetric graphs Homogeneous directed graphs omitting $I \infty$ Propositions $16$ to $20$ and MT $2.2$ Homogeneous directed graphs embedding $I \infty$ Theorems 7.6-7.9 Appendix: Examples for richer languages Bibliography Index of Notation Index.

Product Details

  • ISBN13: 9780821808368
  • Format: Paperback
  • Number Of Pages: 161
  • ID: 9780821808368
  • ISBN10: 0821808362

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