On coherent families of finite-to-one functions

Journal of Symbolic Logic 58 (1):128-138 (1993)


We consider the existence of coherent families of finite-to-one functions on countable subsets of an uncountable cardinal κ. The existence of such families for κ implies the existence of a winning 2-tactic for player TWO in the countable-finite game on κ. We prove that coherent families exist on κ = ωn, where n ∈ ω, and that they consistently exist for every cardinal κ. We also prove that iterations of Axiom A forcings with countable supports are Axiom A

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References found in this work

The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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Citations of this work

Resurrection Axioms and Uplifting Cardinals.Joel David Hamkins & Thomas A. Johnstone - 2014 - Archive for Mathematical Logic 53 (3-4):463-485.
The Bounded Axiom A Forcing Axiom.Thilo Weinert - 2010 - Mathematical Logic Quarterly 56 (6):659-665.

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