Generalizations of the Los-Tarski Preservation Theorem [article]

Abhisekh Sankaran, Bharat Adsul, Supratik Chakraborty
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
more » ... nces in both its extensional and substructural versions. For arbitrary finite vocabularies, we also generalize the extensional version of the Los-Tarski preservation theorem for theories. We also present an interpolant-based approach towards these results. Finally, we present partial results towards generalizing to theories, the substructural version of the Los-Tarski theorem and in the process, we give a preservation theorem that provides a semantic characterization of Σ^0_n theories for each natural number n.
arXiv:1302.4350v2 fatcat:we3ock3knnaelmbrq2z3yly774