On the Hamkins approximation property

Annals of Pure and Applied Logic 144 (1-3):126-129 (2006)
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Abstract

We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property

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10.1016/j.apal.2006.05.005

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A weak variation of Shelah's I[ω₂].William J. Mitchell - 2004 - Journal of Symbolic Logic 69 (1):94-100.

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