INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
congresos y reuniones científicas
Locally finite MV-algebras, multisets and a conjecture of António Aniceto Monteiro
CIGNOLI, ROBERTO LEONARDO OSCAR
Congreso; Colóquio António Aniceto Monteiro; 2007
Sociedade Matemática Portuguesa
: In , Stone duality between Boolean algebras and inverse limits of finite sets is extended to a duality between locally finite MV-algebras and a category of multisets naturally arising as inverse limits of finite multisets. I shall show how this duality specializes to a duality between MVn, the subvariety of MV-algebras generated by the n-element Łukasiewicz chain, and certain Boolean spaces with a distinguished family of closed subsets, for each 2 ≤ n Îw [2, 5]. I will comment the role played by this duality in , where a conjecture of A. A. Monteiro on the structure of maximal subalgebras of algebras in MV3 is proved, and in , where a description of free algebras in MVn over sets of free generators of arbitrary cardinal is given, generalizing a result of A. A. Monteiro for finite sets of free generators. References:  M. Busniche, R. Cignoli, Free MVn-algebras, submitted.  R. Cignoli, Natural dualities for the algebras of Łukasiewicz finitely-valued logics (Abstract), Bulletin of Symbolic Logic, 2 (1996), p. 218.  R. Cignoli, E. J. Dubuc, D. Mundici, Extending Stone duality to multisets and locally finite MV-algebras, Journal of Pure and Applied Algebra, 189 (2004) 37 59.  R. Cignoli, L. Monteiro, Maximal Subalgebras of MVn-algebras. A Proof of a Conjecture of A. Monteiro, Studia Logica, 84 (2006), 393--495.  P. Niederkorn, Natural dualities for varieties of MV-algebras, Journal of Mathematical Analysis and Applications, 225 (2001), 58--73.