PREVIEW OF THE FINAL EXAM

The final exam is scheduled for Tuesday, May 1, from 2 until 3:50. It will cover the following sections from the notes.
1.1-4
2.1,3,4
3.1-4
It will cover the following sections from the book.
1.2-4
2.1-5
3.1-4
4.1-4,6
6.1-5
8.1

AXIOMS

  1. Axiom of Existence
  2. Axiom of Extensionality
  3. Axiom Schema of Separation
  4. Axiom of Pairs
  5. Axiom of Union
  6. Axiom of Power Set
  7. Axiom of Infinity
  8. Axiom Schema of Replacement
  9. Axiom of Regularity
  10. Axiom of Choice

DEFINITIONS

  1. relation
  2. r[a]
  3. r-1[a]
  4. composition of relations
  5. function
  6. compatible functions
  7. one-to-one function
  8. onto function
  9. invertible function
  10. xy
  11. the product of ax for all x in i
  12. equivalence relation
  13. (partial or strict) order
  14. lexicographic order
  15. order isomorphism
  16. well-ordered set
  17. ordinal number
  18. successor ordinal
  19. limit ordinal
  20. inductive set
  21. ordinal addition
  22. ordinal multiplication
  23. ordinal exponentiation
  24. equipotent sets (|x| = |y|)
  25. |x| <= |y|
  26. |x| < |y|
  27. finite set
  28. countable set

THEOREMS

Be familiar with theorems 5, 6, 11, 13, 15, 18, 27, 33, 36, 53, 54, 55, 69, 75, 79, 80, 87, 88, 89, 94, 95, 97-99, 102, 103, 106, 108-112, 114, 116, 118, and 123-125 from the notes.

You should be able to do proofs by induction, and to define functions recursively. I will ask you to define 3 or 4 terms from the list of definitions above, and to repeat the statements of 2 or 3 of the axioms.

I will be available for questions on Thursday afternoon, April 26, until about 3:00, on Friday morning, April 27, until about 1:00, on Monday morning, April 30, until about 11:00, and on Tuesday morning, May 1. You can also email me.