On everywhere strongly logifiable algebras

• Autorzy: Moraschini T.

Identyfikatory

DOI

10.4467/20842589RM.15.006.3915

• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of an everywhere strongly logifiable algebra: a finite non-trivial algebra A such that for every F ∈ P(A) \ {∅,A} the logic determined by the matrix [A, F] is a strongly algebraizable logic with equivalent algebraic semantics the variety generated by A. Then we show that everywhere strongly logifiable algebras belong to the field of universal algebra as well as to the one of logic by characterizing them as the finite non-trivial simple algebras that are constantive and generate a congruence distributive and n-permutable variety for some n ≥ 2. This result sets everywhere strongly logifiable algebras surprisingly close to primal algebras. Nevertheless we shall provide examples of everywhere strongly logifiable algebras that are not primal. Finally, some conclusion on the problem of determining whether the equivalent algebraic semantics of an algebraizable logic is a variety is obtained.

Słowa kluczowe

EN

abstract algebraic logic; strongly algebraizable logic; primal algebra; everywhere strongly logifiable algebra tame congruence theory

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2015
• Tom: Vol. 50
• Strony: 83--107
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Moraschini T.

• Department of logic, history and philosophy of science University of Barcelona (UB) Montalegre 6, E-08001 Barcelona, Spain

Bibliografia

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