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MAD families of projections on l 2 and real-valued functions on ω

MAD families of projections on l 2 and real-valued functions on ω Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [ω] ω and ω ω have been studied for quite some time. In particular, the cardinal invariants $${\mathfrak{a}}$$ and $${\mathfrak{a}_e}$$ , defined to be the minimum cardinality of a maximal infinite almost disjoint family of [ω] ω and ω ω respectively, are known to be consistently less than $${\mathfrak{c}}$$ . Here we examine analogs for functions in $${\mathbb{R}^\omega}$$ and projections on l 2, showing that they too can be consistently less than $${\mathfrak{c}}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

MAD families of projections on l 2 and real-valued functions on ω

Bice, Tristan
Archive for Mathematical Logic , Volume 50 (8) – Sep 4, 2011
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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer-Verlag
Subject
Mathematics; Algebra; Mathematics, general; Mathematical Logic and Foundations
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-011-0249-4
Publisher site
See Article on Publisher Site

Abstract

Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [ω] ω and ω ω have been studied for quite some time. In particular, the cardinal invariants $${\mathfrak{a}}$$ and $${\mathfrak{a}_e}$$ , defined to be the minimum cardinality of a maximal infinite almost disjoint family of [ω] ω and ω ω respectively, are known to be consistently less than $${\mathfrak{c}}$$ . Here we examine analogs for functions in $${\mathbb{R}^\omega}$$ and projections on l 2, showing that they too can be consistently less than $${\mathfrak{c}}$$ .

Journal

Archive for Mathematical Logic – Springer Journals

Published: Sep 4, 2011

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