On the Hamkins approximation property

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 2-Aronszajn trees, and also the "Key Lemma" in Hamkins's gap forcing theorems. The new lemma directly yields Hamkins's newer lemma stating that certain forcing notions have the approximation property. According to Hamkins [2], a partial ordering P satisfies the -approximation property if, whenever A V P is a subset of an ordinal

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: William J. Mitchell
• Keywords: APAL 2006, Certain Forcing Notions, Key Lemma, Main Lemma