Henkin Quantifiers and the Definability of Truth |
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Authors: | Hyttinen Tapani Sandu Gabriel |
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Affiliation: | (1) Department of Mathematics, University of Helsinki, P.O. Box 4, Helsinki, Finland;(2) Department of Philosophy, University of Helsinki, University of Helsinki, P.O. Box 24, 00014, Finland |
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Abstract: | Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension L*1(H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close L*1(H) with respect to Boolean operations, and obtain the language L1(H). At the next level, we consider an extension L*2(H) of L1(H) in which every sentence is an L1(H)-sentence prefixed with a Henkin quantifier. We repeat this construction to infinity. Using the (un)-definability of truth – in – N for these languages, we show that this hierarchy does not collapse. In addition, we compare some of the present results to the ones obtained by Kripke (1975), McGee (1991), and Hintikka (1996). |
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Keywords: | Henkin quantifiers IF logic fixed point logic definability of truth |
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