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Set mappings defined on pairs

Part of: Set theory

Published online by Cambridge University Press:  09 April 2009

N. H. Williams
N. H. Williams
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland, Australia 4067
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Abstract

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A set mapping on pairs over the set S is a function f such that for each unordered pair a of elements of S,f(a) is a subset of S disjoint from a. A subset H of S is said to be free for f if x∉ f({y, z}) for all x, y, z from H. In this paper, we investigate conditions imposed on the range of f which ensure that there is a large set free for f. For example, we show that if f is defined on a set of size K+ + with always |f(a)| <k then f has a free set of size K+ if the range of f satisfies the k-chain condition, or if any two sets in the range of f have an intersection of size less than θ for some θ with θ < K.

MSC classification

Secondary: 03E05: Other combinatorial set theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 356 - 365
Copyright
Copyright © Australian Mathematical Society 1981

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