CS486 Spring 1997

Lecture 21 Thursday, April 10, 1997

• Review (see handout from Moschovakis)
  • defining , alternatives
  • proving the induction principle
  • induction over a well-ordering
  • existence of primitive recursive functions
  • typed lambda notation
• Comparing accounts of numbers and functions
  • and vs and
  • computation rules vs definitions
  • pairs as data vs sets
  • functions as algorithms vs graphs
  • lack of computation in
• Countable (denumerable) and uncountable sets
  • is countable
  • recall Löwenheim theorem
    (Smullyan p.61) on denumerable domaines
  • is uncountable

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