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Über Einen Quantifikator Mit Zwei Wirk Ungsbereichen

In Colloquium on the Foundations of Mathematics, Mathematical Machines and their Applications (1962)

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  1. The Craig Interpolation Theorem in abstract model theory.Jouko Väänänen - 2008 - Synthese 164 (3):401-420.
    The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.
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  • The härtig quantifier: A survey.Heinrich Herre, Michał Krynicki, Alexandr Pinus & Jouko Väänänen - 1991 - Journal of Symbolic Logic 56 (4):1153-1183.
    A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...)
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