A note on syntactical and semantical functions

Studia Logica 46 (2):177 - 185 (1987)
We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class –1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).
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