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Counterexamples of the 0-1 Law for Fragments of Existential Second-Order Logic: an Overview

Published online by Cambridge University Press:  15 January 2014

Jean-Marie Le Bars
Jean-Marie Le Bars*
Affiliation:
Informatique, Greyc, Université De Caen Caen, FranceE-mail:lebars@info.unicaen.fr
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Abstract

We propose an original use of techniques from random graph theory to find a Monadic (Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics (FO2) and] (Minimal Gödel without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the corresponding fragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 6 , Issue 1 , March 2000 , pp. 67 - 82
Copyright
Copyright © Association for Symbolic Logic 2000

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