Abstract logic and set theory. II. large cardinals

Journal of Symbolic Logic 47 (2):335-346 (1982)

Jouko A Vaananen
University of Helsinki
The following problem is studied: How large and how small can the Löwenheim and Hanf numbers of unbounded logics be in relation to the most common large cardinals? The main result is that the Löwenheim number of the logic with the Härtig-quantifier can be consistently put in between any two of the first weakly inaccessible, the first weakly Mahlo, the first weakly compact, the first Ramsey, the first measurable and the first supercompact cardinals
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DOI 10.2307/2273145
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References found in this work BETA

Some Applications of Iterated Ultrapowers in Set Theory.Kenneth Kunen - 1970 - Annals of Mathematical Logic 1 (2):179-227.
A Remark On The Härtig Quantifier.Gebhard Fuhrken - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (13-15):227-228.
A Remark On The Härtig Quantifier.Gebhard Fuhrken - 1972 - Mathematical Logic Quarterly 18 (13‐15):227-228.
Boolean Valued Models and Generalized Quantifiers.Jouko Väänänen - 1980 - Annals of Mathematical Logic 18 (3):193-225.

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