Set theory - an introduction to independence proofs

@inproceedings{Kunen1983SetT,
title={Set theory - an introduction to independence proofs},
author={Kenneth Kunen},
booktitle={Studies in logic and the foundations of mathematics},
year={1983}
}

The Foundations of Set Theory. Infinitary Combinatorics. The Well-Founded Sets. Easy Consistency Proofs. Defining Definability. The Constructible Sets. Forcing. Iterated Forcing. Bibliography. Indexes.

The use of extra-set-theoretic hypotheses, mainly the continuum hypothesis, in the C*-algebra literature are surveyed, and the Calkin algebra emerges as a basic object of interest.Expand

Cardinal and Ordinal Numbers, Topological Preliminaries, Standard Borel Spaces, Selection and Uniformization Theorems, and Analytic and Coanalytic Sets are studied.Expand

We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a… Expand

Abstract In the absence of the Axiom of Choice we study countable families of 2-element sets with no choice functions which either have infinite subfamilies with a choice function or no infinite… Expand

In this paper we prove that the maximum principle in forcing is equivalent to the axiom of choice. We also look at some specic partial orders in the basic Cohen model.

The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver’s theorem and Bukovský’s theorem assert that… Expand