Partition properties of subsets of Pκλ

Masahiro Shioya

ArticleOriginal scientific text

Title

Partition properties of subsets of Pκλ

Authors ¹

Affiliations

Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

Abstract

Let κ > ω be a regular cardinal and λ > κ a cardinal. The following partition property is shown to be consistent relative to a supercompact cardinal: For any

f : \cup_{n < ω} {[X]}^{n}_\subset \to γ

with

X \subset P_{κ} λ

unbounded and 1 < γ < κ there is an unbounded Y ∪ X with

| f'' {[Y]}^{n}_\subset | = 1

for any n < ω.

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Title

Partition properties of subsets of Pκλ

Affiliations

Abstract

Bibliography