Almost everywhere elimination of probability quantifiers

Almost Everywhere Elimination of Probability Quantifiers H. Jerome Keisler and Wafik Boulos Lotfallah

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [9]. This logic has quantifiers like ∃≥3/4y, which says that “for at least 3/4 of all y”. These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifie...

On almost sure elimination of generalized quantifiers

Quantifier Elimination for Neocompact Sets

We shall prove quantifier elimination theorems for neocompact formulas, which define neocompact sets and are built from atomic formulas using finite disjunctions, infinite conjunctions, existential quantifiers, and bounded universal quantifiers. The neocompact sets were first introduced to provide an easy alternative to nonstandard methods of proving existence theorems in probability theory, wh...

Complete Axiomatization of Discrete-Measure Almost-Everywhere Quantification

Following recent developments in the topic of generalized quantifiers, and also having in mind applications in the areas of security and artificial intelligence, a conservative enrichment of (two-sorted) first-order logic with almost-everywhere quantification is proposed. The completeness of the axiomatization against the measure-theoretic semantics is carried out using a variant of the Lindenb...

Almost everywhere domination

A Turing degree a is said to be almost everywhere dominating if, for almost all X ∈ 2 with respect to the “fair coin” probability measure on 2, and for all g : ω → ω Turing reducible to X, there exists f : ω → ω of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We r...