Combining Texts

Ideas for 'fragments/reports', 'What Numbers Are' and 'Investigations in the Foundations of Set Theory I'

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9 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

17608

We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]

17607

Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

10870

ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]

13012

Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]

17609

Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II

13017

Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII

13015

Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation

13020

The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]

13486

Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]