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.