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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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The decidability of ordinal sums
by
Chris Laskowski
Univ of Maryland
Coauthors: Y. V. Shashoua.

The ordinal sum of a family of semigroups indexed by a linear order is discussed in Fuchs [1]. (The universe of the ordinal sum is the disjoint union of the semigroups and the semigroup operation is extended by asserting that x*y=y*x=x whenever y is in a semigroup below the semigroup containing x). We generalize this notion and define the ordinal sum of models of a theory T in any finite language L with no constant symbols. We prove that if T is a decidable L-theory then the class of ordinal sums of models of T is decidable. We then use this result to show that the elementary theory of MV-chains and Hajek's BL-chains [2] are decidable. [1] L. Fuchs, Partially ordered algebraic systems, Addison Wesley, 1963. [2] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer, 1998.

Date received: February 17, 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 # caig-76.