Faculty Publications

Title

Combinatorics for the dominating and unsplitting numbers

Document Type

Article

Journal/Book/Conference Title

Journal of Symbolic Logic

Volume

69

Issue

2

First Page

482

Last Page

498

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{τ, δ}. We derive two corollaries from the proof: τ ≥ min{δ, u} and min{δ, τ} = min{δ, τ}. 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.

Original Publication Date

6-1-2004

DOI of published version

10.2178/jsl/1082418539

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