Journal of Philosophical Logic

, Volume 29, Issue 5, pp 507–527

Henkin Quantifiers and the Definability of Truth

  • Tapani Hyttinen
  • Gabriel Sandu

DOI: 10.1023/A:1026533210855

Cite this article as:
Hyttinen, T. & Sandu, G. Journal of Philosophical Logic (2000) 29: 507. doi:10.1023/A:1026533210855


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 truthin – 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).

Henkin quantifiersIF logicfixed point logicdefinability of truth

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Tapani Hyttinen
    • 1
  • Gabriel Sandu
    • 2
  1. 1.Department of MathematicsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of Philosophy, University of HelsinkiUniversity of HelsinkiFinland