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On coherent families of finite-to-one functions

Published online by Cambridge University Press:  12 March 2014

Piotr Koszmider
Piotr Koszmider*
Affiliation:
Department of Mathematics, York University, North York, Ontario, Canada, M3J 1P3, E-mail: piotr@clid.yorku.ca
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 128 - 138
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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