WEEK 1

M: No lecture.
W: Motivation for set theory. Language of set theory. Zermelo-Fraenkel axioms:
      Existence, Extensionality, Foundation, Pairing, Union.
     1.1. Definition. Formula.
     1.2. Definition. Free and bound occurence of a variable.
     1.3. Definition. Sentence.
F: Completion of the list of axioms: Infinity, Separation, Replacement and Power Set. Axiomatic systems
     ZF, Z and ZF -- A. Successor, the empty set. Subset, proper subset, power set. Class, proper class.
    1.4. Proposition and Definition. S(x).
    1.5. Proposition and Definition. The empty set.
    1.6. Definition. Ordered pair <x,y>.
    1.7. Proposition. <x,y> = <x',y'>  iff  (x = x' and y = y').
    1.8. Definition. Class, proper class.
    1.9. Proposition. V is a proper class.