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Ultraproducts of Z with an Application to Many-Valued Logics

✍ Scribed by Joan Gispert i Brasó; Daniele Mundici; Antoni Torrens Torrell

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
140 KB
Volume
219
Category
Article
ISSN
0021-8693

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✦ Synopsis

Up to categorical equivalence, abelian lattice-ordered groups with strong unit coincide with Chang's MV-algebrasᎏthe Lindenbaum algebras of the infinite-valued Łukasiewicz calculus. While the property of being a strong unit is not definable even in first-order logic, MV-algebras form an equational class. On the other hand, the addition operation and the translation invariant lattice order of a lattice-ordered group are more amenable than the truncated addition operation of an MV-algebra. In this paper MV-algebraic and group-theoretical techniques are combined to classify and axiomatize all universal classes generated by an infinite totally ordered * Partially supported by Grants Nos. FIr94-1351 and SGRr96-00052 of DGR of Generalitat de Catalunya and by Grant No. PB97-0888 of DGICYT of Spain and by COST ACTION 15 on many-valued logics for computer science applications.

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