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Generalizations of the Los-Tarski Preservation Theorem
[article]
2013
arXiv
pre-print
We present new preservation theorems that semantically characterize the ∃^k ∀^* and ∀^k ∃^* prefix classes of first order logic, for each natural number k. Unlike preservation theorems in the literature that characterize the ∃^* ∀^* and ∀^* ∃^* prefix classes, our theorems relate the count of quantifiers in the leading block of the quantifier prefix to natural quantitative properties of the models. As special cases of our results, we obtain the classical Los-Tarski preservation theorem for
arXiv:1302.4350v2
fatcat:we3ock3knnaelmbrq2z3yly774