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Failure of interpolation for quantifiers of monadic type

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Methods in Mathematical Logic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1130))

Abstract

It is shown that no proper extension of first order logic by Lindström-Mostowski quantifiers of monadic type, that is quantifiers of the form Qx1…xn(ф1(x1),…,фn(xn)), satisfies the many sorted Craig’s interpolation lemma or even the one sorted, if closed under relativizations. For example Lω1ω or any of its admissible fragments can not be generated by any number of these quantifiers. This generalizes previous results of the same type shown under stronger hypothesis. In contrast, all monadic logics generated by cardinal quantifiers satisfy interpolation.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de los Andes, Apartado Aéreo 4976, Botogtá D.E., Colombia

    Xavier Caicedo

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  1. Xavier Caicedo
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Carlos Augusto Di Prisco

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© 1985 Springer-Verlag

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Caicedo, X. (1985). Failure of interpolation for quantifiers of monadic type. In: Di Prisco, C.A. (eds) Methods in Mathematical Logic. Lecture Notes in Mathematics, vol 1130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075304

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  • DOI: https://doi.org/10.1007/BFb0075304

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15236-1

  • Online ISBN: 978-3-540-39414-3

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