Ultraproducts and Their Topological Structure
by
Gábor Sági
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences

As was recognised in [1], ultraproducts preserving the validity of certain higher order formulas can be characterized in terms of some topological spaces (which are called ultratopologies). Ultratopologies provide a natural extra structure for ultraproducts and studying this extra structure is useful just for purely model theoretic and algebraic reasons. We will illustrate this by presenting some recently obtained connection between topological and model theoretical properties of ultraproducts. In addition, some results about automorphism groups of finite structures will also be established.

References

[1] G. Sági, Ultraproducts and Higher Order Formulas, Math. Log. Quart., 48 (2002) 2, pp.261-275.

[2] J. Gerlits, G. Sági, Ultratopologies, Manuscript, in preparation, 2002.

Date received: June 28, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiv-34.