Set theory - an introduction to independence proofs

  title={Set theory - an introduction to independence proofs},
  author={Kenneth Kunen},
  booktitle={Studies in logic and the foundations of mathematics},
  • K. Kunen
  • Published in
    Studies in logic and the…
    15 December 1983
  • Mathematics
The Foundations of Set Theory. Infinitary Combinatorics. The Well-Founded Sets. Easy Consistency Proofs. Defining Definability. The Constructible Sets. Forcing. Iterated Forcing. Bibliography. Indexes. 

A Note on Transitive Sets without the Foundation Axiom

  • M. Kysiak
  • Economics, Mathematics
    Reports Math. Log.
  • 2006
A model of set theory without the foundation axiom in which there exists a transitive set whose intersection is not transitive is constructed.

Definable MAD families and forcing axioms

Set Theory and C*-Algebras

  • N. Weaver
  • Mathematics
    Bulletin of Symbolic Logic
  • 2007
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.

A Course on Borel Sets

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

The Theory of Sets of Ordinals

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

On Russell and Anti Russell-Cardinals

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

The maximum principle in forcing and the axiom of choice

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.

Martin's Axiom and embeddings of upper semi-lattices into the Turing degrees

  • Wang Wei
  • Computer Science
    Ann. Pure Appl. Log.
  • 2010

On the Set-Generic Multiverse

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