The eskolemization of universal quantifiers

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Abstract

This paper is a sequel to the papers Baaz and Iemhoff (2006, 2009) [4], [6] in which an alternative skolemization method called eskolemization was introduced that, when restricted to strong existential quantifiers, is sound and complete for constructive theories. In this paper we extend the method to universal quantifiers and show that for theories satisfying the witness property it is sound and complete for all formulas. We obtain a Herbrand theorem from this, and apply the method to the intuitionistic theory of equality and the intuitionistic theory of monadic predicates.

MSC

03F07
03F50
03F03
03F55

Keywords

Skolemization
Herbrand’s theorem
Constructive theories
Intuitionistic logic

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