Abstract
The present paper defines the concept of a partially interpreted generalized quantifier and studies some of the basic model-theoretic properties of the resulting logic. As such, the paper continues and completes a line of research started by Kripke (1975) and continued by Feferman (1984), van Benthem (1985), Blarney (1986), and Langholm (1988) which studied the logic of partially interpreted predicates. Surprisingly enough, the logic studied here which combines the partial interpretation of predicates with that of quantifiers turns out to have very nice abstract properties: Compactness, the Lövenheim-Skolem Properties, an effective Interpolation Property, and the property that it defines its own truth-predicate.
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Sandu, G. (2003). Partially Interpreted Henkin Quantifiers. In: Hintikka, J., Czarnecki, T., Kijania-Placek, K., Placek, T., Rojszczak, A. (eds) Philosophy and Logic in Search of the Polish Tradition. Synthese Library, vol 323. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0249-2_8
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DOI: https://doi.org/10.1007/978-94-017-0249-2_8
Publisher Name: Springer, Dordrecht
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