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15 - Proper Forcing and PFA

from Part II - What is New in Set Theory

Published online by Cambridge University Press:  28 September 2020

Mirna Džamonja
Mirna Džamonja
Affiliation:
Institute for the History and Philosophy of Science and Technology, Paris
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Summary

A new chapter in the theory of forcing was opened by Shelah’s discovery of proper forcing in [100]. The novelty of Shelah’s approach is a move from infinite combinatorics to the technique of elementary submodels, which has since integrated set theory to the extent that it is hard to imagine a forcing argument that does not use it. A major reference on the technique and results about proper forcing is Shelah’s book [105]. Throughout this chapter, we fix an uncountable regular cardinal χ which is so large that all arguments relative to the forcing notions we discuss are contained in the set H(χ) of all sets x with |TC(x)| < χ.

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Fast Track to Forcing , pp. 90 - 103
Publisher: Cambridge University Press
Print publication year: 2020

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