Ideas of John von Neumann, by Theme
[Hungarian, 1903  1957, One of the fathers of the modern computer.]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340

Von Neumann defines each number as the set of all smaller numbers [Blackburn]

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943

Limitation of Size is not selfevident, and seems too strong [Lavine]

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355

Von Neumann wanted mathematical functions to replace sets [Benardete,JA]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489

Von Neumann treated cardinals as a special sort of ordinal [Hart,WD]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
12336

A von Neumann ordinal is a transitive set with transitive elements [Badiou]

22716

Von Neumann defined ordinals as the set of all smaller ordinals [Poundstone]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18180

Von Neumann numbers are preferred, because they continue into the transfinite [Maddy]

18179

For Von Neumann the successor of n is n U {n} (rather than {n}) [Maddy]

15925

Each Von Neumann ordinal number is the set of its predecessors [Lavine]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672

All the axioms for mathematics presuppose set theory
