Existential Vs Preserved by Extensions, and Other Syntax/semantics Correspondences

We look at various preservation theorems of classical logic ((rst of all, Los-Tarski theorem) which fail in the context of nite models , and examine the extent of their failure. In some cases, even if the old correspondence between syntactical and semantical properties does not hold, one can nd a new semantical counterpart for the syntacti-cal property, and vice versa-a new syntactical counterpart for the semantical property.