FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 7, PAGES 179-203

**Hypergraphs of prime models and distributions of countable models of
small theories**

S. V. Sudoplatov

Abstract

View as HTML
View as gif image

Hypergraphs of prime models over realizations of types in small
theories are defined.
On the basis of graph structures of models of small theories,
hierarchies of sets in these hypergraphs, revealing structural
connections in countable models of small theories, are established.
The key role of graph-theoretic objects in constructions of
Ehrenfeucht theories is proved.
Using hypergraph constructions, a classification of complete
first-order theories with finite Rudin--Keisler preorders is
generalized to the class of all small theories.

Location: http://mech.math.msu.su/~fpm/eng/k09/k097/k09709h.htm

Last modified: April 18, 2010