Computer Science > Logic in Computer Science
[Submitted on 10 Jul 2020 (v1), last revised 24 Oct 2020 (this version, v2)]
Title:Extension Preservation in the Finite and Prefix Classes of First Order Logic
View PDFAbstract:It is well known that the classic Łoś-Tarski preservation theorem fails in the finite: there are first-order definable classes of finite structures closed under extensions which are not definable (in the finite) in the existential fragment of first-order logic. We strengthen this by constructing for every $n$, first-order definable classes of finite structures closed under extensions which are not definable with $n$ quantifier alternations. The classes we construct are definable in the extension of Datalog with negation and indeed in the existential fragment of transitive-closure logic. This answers negatively an open question posed by Rosen and Weinstein.
Submission history
From: Abhisekh Sankaran [view email][v1] Fri, 10 Jul 2020 16:00:00 UTC (18 KB)
[v2] Sat, 24 Oct 2020 17:08:45 UTC (18 KB)
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