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Sixth Annual Conference in Ordered Algebraic Structures
March 5-8, 2003
Department of Mathematics, Vanderbilt University
Nashville, TN, USA

Organizers
Jorge Martinez, University of Florida and Constantine Tsinakis, Vanderbilt University

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Complete finite first-order theories of chains
by
Trevor Green
University of Saskatchewan
Coauthors: François Dorais (Dartmouth College)

A first-order theory in the language of chains (totally ordered sets) is complete if all chains that satisfy the axioms of the theory satisfy exactly the same first-order formulæ. We call a complete theory n-complete if none of its axioms contains more than n variables. Chains that satisfy such a theory also form an equivalence class when considered from the viewpoint of n-move Ehrenfeucht-Fraïssé games, and using techniques from this area, we shall present an O(exp(exp(n))) lower bound on the number of distinct n-complete theories, as well as some preliminary results on the "completeness level" of various sums of chains.

Date received: December 31, 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 # cakg-20.