On Skolemization in constructive theories

Journal of Symbolic Logic 73 (3):969-998 (2008)
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
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DOI 10.2178/jsl/1230396760
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Rosalie Iemhoff (2010). The Eskolemization of Universal Quantifiers. Annals of Pure and Applied Logic 162 (3):201-212.

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