Failure of interpolation for quantifiers of monadic type

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 an...

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Bibliographic Details
Main Author: Caicedo, Xavier
Format: Book Chapter
Language:English
Subjects:
Extension Property
Monadic Predicate
Partial Isomorphism
Proper Extension
Strong Limit Cardinal
Online Access:Get full text
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Summary: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.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0075304