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A note on syntactical and semantical functions
Authors:Adam Gajda  Michał Krynicki  Lesław Szczerba
Affiliation:(1) Institute of Mathematics, The Branch of University of Warsaw, 15-267 Bia"lstrok"ystok, Poland;(2) Institute of Mathematics, University of Warsaw, PKiN, Warsaw, Poland
Abstract:We say that a semantical function Gcy is correlated with a syntactical function F iff for any structure A and any sentence phiv we have A models Fphiv harr GammaA models phiv.It is proved that for a syntactical function F there is a semantical function Gcy correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function Gcy there is a syntactical function F correlated with Gcy iff for any finitely axiomatizable class X the class Gcy–1X is also finitely axiomatizable (i.e. iff Gcy is continuous in model class topology).
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