Journal of Symbolic Logic

Asymptotic Probabilities for Second-Order Existential Kahr-Moore-Wang Sentences

Anne Vedo

Abstract

We show that the 0-1 law does not hold for the class $\Sigma^1_1 (\forall\exists\forall \text{without} =)$ by finding a sentence in this class which almost surely expresses parity. We also show that every recursive real in the unit interval is the asymptotic probability of a sentence in this class. This expands a result by Lidia Tendera, who in 1994 proved that every rational number in the unit interval is the asymptotic probability of a sentence in the class $\Sigma^1_1 \forall\exists\forall$ with equality.

Article information

Source
J. Symbolic Logic, Volume 62, Issue 1 (1997), 304-319.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745196

Mathematical Reviews number (MathSciNet)
MR1450525

Zentralblatt MATH identifier
0880.03016

JSTOR