P. Komjáth, V. Totik

Problems and Theorems in Classical Set Theory

Contents

  1. Operations on sets
  2. Countability
  3. Equivalence
  4. Continuum
  5. Sets of reals and real functions
  6. Ordered sets
  7. Order types
  8. Ordinals
  9. Ordinal arithmetic
  10. Cardinals
  11. Partially ordered sets
  12. Transfinite enumeration
  13. Euclidean spaces
  14. Zorn's Lemma
  15. Hamel bases
  16. The continuum hypothesis
  17. Ultrafilters on ω
  18. Families of sets
  19. The Banach-Tarski paradox
  20. Stationary sets in ω1
  21. Stationary sets in larger cardinals
  22. Canonical functions
  23. Infinite graphs
  24. Partition relations
  25. Δ-systems
  26. Set mappings
  27. Trees
  28. The measure problem
  29. Stationary sets in [λ]
  30. The axiom of choice
  31. Well founded sets and the axiom of foundation