Journal of Symbolic Logic

On Skolemization in constructive theories

Matthias Baaz and Rosalie Iemhoff

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Abstract

In this paper a method for the replacement, in formulas, of strong quantifiers by functions is introduced that can be considered as an alternative to Skolemization in the setting of constructive theories. A constructive extension of intuitionistic predicate logic that captures the notions of preorder and existence is introduced and the method, orderization, is shown to be sound and complete with respect to this logic. This implies an analogue of Herbrand’s theorem for intuitionistic logic. The orderization method is applied to the constructive theories of equality and groups.

Article information

Source
J. Symbolic Logic Volume 73, Issue 3 (2008), 969-998.

Dates
First available: 27 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1230396760

Digital Object Identifier
doi:10.2178/jsl/1230396760

Mathematical Reviews number (MathSciNet)
MR2444281

Zentralblatt MATH identifier
05531011

Citation

Baaz, Matthias; Iemhoff, Rosalie. On Skolemization in constructive theories. Journal of Symbolic Logic 73 (2008), no. 3, 969--998. doi:10.2178/jsl/1230396760. http://projecteuclid.org/euclid.jsl/1230396760.


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