Hierarchies of monadic generalized quantifiers

Hierarchies of monadic generalized quantifiers

A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig qua...

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Veröffentlicht in:The Journal of symbolic logic 2000-09, Vol.65 (3), p.1241-1263
1. Verfasser: Luosto, Kerkko
Format: Artikel
Sprache:eng
Schlagworte:
03C13
03C80
05D10
Boolean data
Cardinality
Cartesianism
Integers
Logical theorems
Mathematical theorems
Mathematics
Monoids
Natural numbers
Quantifier elimination
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Zusammenfassung:A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory.
ISSN:0022-4812
1943-5886
DOI:10.2307/2586699