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Ultrafilters on spaces of partitions

Q κ λ . P κ λ the space of all < κ -sized subsets of λ , has provided numerous opportunities for the gainful employment of set theorists in recent years, thanks to its combinatorial richness and to its relationships with various large cardinals. In the spirit of P κ λ we offer the following defin...

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Bibliographic Details
Published in:The Journal of symbolic logic 1982-03, Vol.47 (1), p.137-146
Main Authors: Henle, James M., Zwicker, William S.
Format: Article
Language:English
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Summary:Q κ λ . P κ λ the space of all < κ -sized subsets of λ , has provided numerous opportunities for the gainful employment of set theorists in recent years, thanks to its combinatorial richness and to its relationships with various large cardinals. In the spirit of P κ λ we offer the following definition: For κ ≤ λ both cardinals, Q κ λ is the set of all partitions of λ into < κ -many pieces (an element of q ∈ Q κ λ is called a piece of q ). Equivalently An element of P κ λ may be viewed as an injection from a < κ -sized set into λ , with some information thrown away. An element of Q κ λ is a surjection from λ onto a < κ -sized set, with analogous loss of information. For p, q ∈ Q κ λ , we say p ≤ q iff q is a refinement of p (every piece of q is contained in a piece of p ).
ISSN:0022-4812
1943-5886
DOI:10.2307/2273387