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Free algebras in varieties of BL-algebras generated by a BLn-chain

Part of: Algebraic logic General logic Computability and recursion theory Varieties

Published online by Cambridge University Press:  09 April 2009

Manuela Busaniche  and
Roberto Cignoli
Manuela Busaniche
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires - CONICET, Ciudad Universitaria, 1428 Buenos Aires, Argentina, e-mail: manuelabusaniche@yahoo.com.ar, cignoli@mate.dm.uba.ar
Roberto Cignoli
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires - CONICET, Ciudad Universitaria, 1428 Buenos Aires, Argentina, e-mail: manuelabusaniche@yahoo.com.ar, cignoli@mate.dm.uba.ar
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Abstract

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Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln, and a generalized BL-chain B are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of Ln, and free algebras in the variety of basic hoops generated by B. The Boolean products are taken over the Stone spaces of the Boolean subalgebras of idempotents of free algebras in the variety of MV-algebras generated by Ln.

2000 Mathematics subject classification: primary 03G25, 03B50, 03B52, 03D35, 03G25, 08B20.

Keywords

03G25BL-algebrasresiduated latticeshoopsMoisil algebrasfree algebrasBoolean products.

MSC classification

Secondary: 03G25: Other algebras related to logic 03B50: Many-valued logic 03B52: Fuzzy logic; logic of vagueness 03D35: Undecidability and degrees of sets of sentences 08B20: Free algebras

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 3 , June 2006 , pp. 419 - 439
Copyright
Copyright © Australian Mathematical Society 2006

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