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The Suszko operator relative to truth‐equational logics
Author(s) -
Albuquerque Hugo
Publication year - 2021
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000034
Subject(s) - mathematics , operator (biology) , equational logic , representation (politics) , class (philosophy) , discrete mathematics , algebra over a field , pure mathematics , computer science , programming language , artificial intelligence , rewriting , biochemistry , chemistry , repressor , gene , politics , transcription factor , political science , law
This note presents some new results from [1] about the Suszko operator and truth‐equational logics, following the works of Czelakowski [11] and Raftery [17]. It is proved that the Suszko operator relative to a truth‐equational logic S preserves suprema and commutes with endomorphisms. Together with injectivity, proved by Raftery in [17], the Suszko operator relative to a truth‐equational logic is a structural representation, as defined in [15]. Furthermore, if Alg ( S ) is a quasivariety, then the Suszko operator relative to a truth‐equational logic is continuous. Finally, it is proved that truth is equationally definable in the classLMod Su ( S )if and only if Alg ( S ) is a τ∞ ‐algebraic semantics for S and the Suszko operatorΩ ∼ S Fm : Th S → Co Alg ( S ) Fm preserves suprema and commutes with substitutions.