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June 2004 Combinatorics for the dominating and unsplitting numbers
Jason Aubrey
J. Symbolic Logic 69(2): 482-498 (June 2004). DOI: 10.2178/jsl/1082418539

Abstract

In this paper we introduce a new property of families of functions on the Baire space, called pseudo-dominating, and apply the properties of these families to the study of cardinal characteristics of the continuum. We show that the minimum cardinality of a pseudo-dominating family is min{𝖗, 𝖉}. We derive two corollaries from the proof: 𝖗 ≥ min{ 𝖉, 𝖚 } and min{ 𝖉, 𝖗 } = min{ 𝖉, 𝖗_σ }. We show that if a dominating family is partitioned into fewer that 𝖘 pieces, then one of the pieces is pseudo-dominating. We finally show that 𝖚 < 𝖌 implies that every unbounded family of functions is pseudo-dominating, and that the Filter Dichotomy principle is equivalent to every unbounded family of functions being finitely pseudo-dominating.

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Jason Aubrey. "Combinatorics for the dominating and unsplitting numbers." J. Symbolic Logic 69 (2) 482 - 498, June 2004. https://doi.org/10.2178/jsl/1082418539

Information

Published: June 2004
First available in Project Euclid: 19 April 2004

zbMATH: 1069.03038
MathSciNet: MR2058185
Digital Object Identifier: 10.2178/jsl/1082418539

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 2 • June 2004
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