# Philosophy Lexicon of Arguments

Author Item Excerpt Meta data
Basieux, P.

Books on Amazon
Set Theory Ba I 86
Axioms of the Set Theory/Halmos/Basieux: 1) extensionality axiom: two sets are only equal iff they have the same elements - 2) selection axiom: for every set A and every condition (or property) E(x) there is a set B, whose elements are exactly every x of A, for which E(x) applies - 3) pairing axiom: for every two sets there is always one set that contains those two as elements - 4) combination axiom: for every set system there is a set that contains all elements that belong to at least one set of the given system - 5) power set axiom: for every quantity there is a set system that contains all the subsets of the given set among its elements - 6) infinity axiom: there is a set that contains the empty set and with each of its elements also its successor - 7) choice axiom: the Cartesian product of a (non-empty) system of non-empty sets is non-empty - 8) replacement axiom: S(a,b) be a statement of the kind that for each element a of a set A the set {b I S (a,b)} can be formed. Then there is a function F with domain A such that F(a) = {b I S(a,b)} for every a in A -