Studia Logica 44 (3):257 - 264 (1985)
AbstractIn paper  it was shown that a great part of model theory of logic with the generalized quantifier Q x = there exist uncountably many x is reducible to the model theory of first order logic with an extra binary relation symbol. In this paper we consider when the quantifier Q x can be syntactically defined in a first order theory T. That problem was raised by Kosta Doen when he asked if the quantifier Q x can be eliminated in Peano arithmetic. We answer that question fully in this paper.
Similar books and articles
Arithmetic Definability by Formulas with Two Quantifiers.Shih Ping Tung - 1992 - Journal of Symbolic Logic 57 (1):1-11.
Definability and Quantifier Elimination for J3-Theories.Ítala M. L. D'Ottaviano - 1987 - Studia Logica 46 (1):37 - 54.
Henkin Quantifiers and the Definability of Truth.Tapani Hyttinen & Gabriel Sandu - 2000 - Journal of Philosophical Logic 29 (5):507-527.
Generalized Quantifiers and Modal Logic.Wiebe Van Der Hoek & Maarten De Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.
Regularity in Models of Arithmetic.George Mills & Jeff Paris - 1984 - Journal of Symbolic Logic 49 (1):272-280.
Characterizing Definability of Second-Order Generalized Quantifiers.Juha Kontinen & Jakub Szymanik - 2011 - In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Added to PP
Historical graph of downloads
Citations of this work
Generalized Quantification as Substructural Logic.Natasha Alechina & Michiel Van Lambalgen - 1996 - Journal of Symbolic Logic 61 (3):1006 - 1044.
European Summer Meeting of the Association for Symbolic Logic, Paris, 1985.K. R. Apt - 1987 - Journal of Symbolic Logic 52 (1):295-349.
References found in this work
Logic with the Quantifier “There Exist Uncountably Many”.H. Jerome Keisler - 1970 - Annals of Mathematical Logic 1 (1):1-93.
Logic with the Quantifier "There Exist Uncountably Many".H. Jerome Keisler - 1970 - Annals of Mathematical Logic 1 (1):1.
Regular Relations and the Quantifier “There Exist Uncountably Many”.Zarko Mijajlović & Valentina Harizanov - 1983 - Mathematical Logic Quarterly 29 (3):151-161.