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D.I. Saveliev, V.B. Shehtman

Axiomatic set theory

  1. Summary of the previous course "Basic set theory".
  2. Cofinality. Regular and singular cardinals.
  3. Inaccessible cardinals. Measurable cardinals.
  4. Games and strategies. The Axiom of Determinateness.
  5. Transitive models.
  6. Constructive sets.
  7. Forcing.
  8. Independence of Continuum Hypothesis.
  9. Independence of Axiom of Choice.

Bibliography

  1. C. Kuratowski, A. Mostowski. Set theory. Amsterdam, 1968.
  2. A. Levy. Basic set theory. Springer, 1979.
  3. D. van Dalen, H.C. Doets, H. de Swart. Sets: naive, axiomatic and applied. Pergamon Press, 1978.
  4. M. Fitting, R. Smullyan. Set theory and the continuum problem. Oxford University Press, 1996.
  5. T. Jech. Set theory. Springer, 2002
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