On the Expressive Power of the Language Using the Henkin Quantifier

  • M. Krynicki
Part of the Synthese Library book series (SYLI, volume 122)


Investigations of languages with additional quantifiers have a rather long history. This history starts in 1957 with Mostowski’s paper [9]. Next, Fuhrken [1, 2] Keisler [6] and Slomson [10] investigated properties of the language with such quantifiers as ‘there exist infinitely many’, ‘there exist uncountably many’, ‘there exist as many as all elements’ etc. In [3] Henkin proposed to investigate the quantifier which arose by writing the existential and universal quantifier parallel. Some people (see e.g. [4]) used this idea to construct a language and investigate its properties, mainly the syntactical properties. Only in [11] we find remarks about a connection between the quantifier defined by Henkin and other quantifiers. In this paper I want to throw some light on the semantical properties of the language with the quantifier defined in [3] and especially on its connection with the second order logic. These results were obtained in collaboration with Professor A. W. Lachlan and will be published in detail. I use the standard model theoretical notation as in [11].


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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1979

Authors and Affiliations

  • M. Krynicki
    • 1
  1. 1.Department of MathematicsUniversity of WarsawPoland

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