Tameness in least fixed-point logic and McColm's conjecture release_utqawsoin5bqvoyeyrf3na4ame

by Siddharth Bhaskar, Alex Kruckman

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2017  

Abstract

We investigate fundamental model-theoretic dividing lines (the order property, the independence property, the strict order property, and the tree property 2) in the context of least fixed-point (LFP) logic over families of finite structures. We show that, unlike the first-order (FO) case, the order property and the independence property are equivalent, but all of the other natural implications are strict. We identify the LFP strict order property with proficiency, a well-studied notion in finite model theory. Gregory McColm conjectured that FO and LFP definability coincide over a family C of finite structures exactly when C is non-proficient. McColm's conjecture is false in general, but as an application of our results, we show that it holds under standard FO tameness assumptions adapted to families of finite structures.
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Date   2017-08-01
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arXiv  1708.00148v1
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