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Ideas of John von Neumann, by Text

[Hungarian, 1903 - 1957, One of the fathers of the modern computer.]

1923 On the Introduction of Transfinite Numbers
p.24 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy]
p.24 For Von Neumann the successor of n is n U {n} (rather than {n}) [Maddy]
p.73 Von Neumann treated cardinals as a special sort of ordinal [Hart,WD]
p.122 Each Von Neumann ordinal number is the set of its predecessors [Lavine]
p.128 A von Neumann ordinal is a transitive set with transitive elements [Badiou]
1925 An Axiomatization of Set Theory
p.209 All the axioms for mathematics presuppose set theory
p.215 Limitation of Size is not self-evident, and seems too strong [Lavine]
1935 works
p.29 Von Neumann defined ordinals as the set of all smaller ordinals [Poundstone]
p.188 Von Neumann wanted mathematical functions to replace sets [Benardete,JA]
p.280 Von Neumann defines each number as the set of all smaller numbers [Blackburn]