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Basic set theory (Spring 2003)

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В.Б.Шехтман, Д.И.Савельев

Основы теории множеств

Программа курса

  1. Axioms of set theory in different versions: ZF, NBG, TT.
  2. The simplest set-theoretic notions (relation, function, product etc.)
  3. Natural numbers. Finite and infinite sets. Countable sets.
  4. Well-orderings. Ordinals and their properties. Transfinite induction.
  5. Cardinalities. Cantor- Bernstein theorem. Cantor theorem.
  6. Axiom of Choice and Zermelo theorem. Zorn's lemma. Filters and ultrafilters.
  7. Cardinals. Cardinal arithmetic.
  8. Cofinality. Regular and singular cardinals.
  9. Generalized continuum hypothesis. Sierpinsky theorem.
  10. Inaccessible cardinals. Measurable cardinals.
  11. Games and strategies. The axiom of Determinateness.

Bibliography

  1. C. Kuratowski, A. Mostowski. Set theory. Amsterdam, 1968.
  2. A. Levy. Basic set theory. Springer, 1979.
  3. M. Zuckerman. Sets and transfinite numbers. Macmillan, 1974.
  4. D. van Dalen, H.C. Doets, H. de Swart. Sets: naive, axiomatic and applied. Pergamon Press, 1978.
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