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A Generalization of the Łoś-Tarski Preservation Theorem
[article]
2016
arXiv
pre-print
In this dissertation, we present for each natural number k, semantic characterizations of the ∃^k ∀^* and ∀^k ∃^* prefix classes of first order logic sentences, over all structures finite and infinite. This result, that we call the *generalized Łoś-Tarski theorem*, abbreviated GLT(k), yields the classical Łoś-Tarski preservation theorem when k equals 0. It also provides new characterizations of the Σ^0_2 and Π^0_2 prefix classes, that are finer than all characterizations of these classes in the
arXiv:1609.06297v1
fatcat:6kucahkypzet3mm3kxpwjhu7py