The equational definability of truth predicates

• Autorzy: Raftery J. G.
• Języki publikacji: EN

Abstrakty

EN

Let S be a structural consequence relation, not assumed to be protoalgebraic. It is proved that the following con- ditions on S are equivalent, where `algebra' means algebra in the signature of S: (1) S is truth-equational, i.e., the truth predicate of the class of reduced matrix models of S is explicitly denable by some xed set of unary equations. (2) The Leibniz operator of S is completely order re ecting on all algebras, i.e., for any set of S{lters F [ fGg of an algebra, if T [F] G then TF G. (3) The Leibniz operator is completely order re ecting on the theories of S. (4) The Suszko operator of S is injective on all algebras. It makes no dierence to the meaning of (1) whether `reduced' is interpreted as Leibniz-reduced or as Suszko-reduced. For the class of Suszko-reduced matrix models of S, (4) ) (1) says that the im- plicit denability of the truth predicate entails its equational de- nability. Previously, this was known only for protoalgebraic sys- tems. The corresponding assertion for the Leibniz-reduced models is shown to be false, i.e., global injectivity of the Leibniz operator does not entail truth-equationality.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2006
• Tom: Nr 41,spec. iss.
• Strony: 95--149
• Opis fizyczny: Bibliogr. 51 poz.

Twórcy

autor

Raftery J. G.

• School of Mathematical Sciences University of KwaZulu-Natal Durban 4001, South Africa,

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