Paper: Fragments of Existential Second-Order Logic without 0-1 Laws (at LICS 1998)

Authors: Jean-Marie Le Bars

Abstract

We prove that there is a Monadic Σ₁¹ (Minimal Scott without equality) sentence without an asymptotic probability. Our result entails that the 0-1 law fails for the logics Σ₁¹(FO²) and Σ₁ ¹ (Minimal Godel without equality). Therefore we achieve the classification of first-order prefix classes with or without equality. According to the existence of the 0-1 law for the corresponding Σ ₁¹ 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

BibTeX

  @InProceedings{LeBars-FragmentsofExistent,
    author = 	 {Jean-Marie Le Bars},
    title = 	 {Fragments of Existential Second-Order Logic without 0-1 Laws},
    booktitle =  {Proceedings of the Thirteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1998)},
    year =	 {1998},
    month =	 {June}, 
    pages =      {525--536 },
    location =   {Indianapolis, IN, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }