Journal of Philosophical Logic 29 (5):507-527 (2000)

Gabriel Sandu
University of Helsinki
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)
Keywords Henkin quantifiers  IF logic  fixed point logic  definability of truth
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Reprint years 2004
DOI 10.1023/A:1026533210855
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References found in this work BETA

Quantifiers Vs. Quantification Theory.Jaakko Hintikka - 1973 - Dialectica 27 (3‐4):329-358.
Infinistic Methods.L. Henkin - 1961 - Pergamon Press.

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Independence Friendly Logic.Tero Tulenheimo - 2010 - Stanford Encyclopedia of Philosophy.
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