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Priestley spaces of free MV-algebras
by
Leonardo Manuel Cabrer
CONICET - Universidad Nacional del Centro - Buenos Aires - Argentina
In [1] Panti describes prime ideals of free MV-algebras, by characterizing the prime ideals of free l-groups. In [2] Busaniche and Mundicci develop a different characterization using the geometric nature of the McNaughton's representation of free MV-algebras.
Following these ideas, in this work we will give a geometric description of the Priestley spaces of the lattice reducts of the free MV-algebras with finite number of generators. This description involves a characterization of the set of prime lattice filters of the free MV-algebra and its topology. These lattice filters are related with the prime theories of the semilattice based deductive system introduced and studied in [3].
[1] G. Panti, Prime Ideals in Free l-groups and the Free Vector Lattices,
Journal of Algebra 219 (1999) 173-200.
[2] M. Busaniche and D. Mundici, Geometry of Robinson Consistency in Lukasiewicz Logic, Annals of Pure and Applied Logic (2007), doi:10.1016/j.apal.2006.11.003
[3] J.M. Font, À .J. Gil, A. Torrens and V. Verdú, On the Infinite-Valued Lukasiewicz Logic that Preserves Degrees of Truth, Archive for Mathematical Logic, 2006 , 45 , 839-868.
Date received: May 14, 2007
Copyright © 2007 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 # caug-59.