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Dependent choice, ‘quote’ and the clock

✍ Scribed by Jean-Louis Krivine


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
302 KB
Volume
308
Category
Article
ISSN
0304-3975

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📜 SIMILAR VOLUMES


Dependent Choices and Anti-Foundation
✍ Hisato Muraki 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 267 KB

In Zermelo-Fraenkel set theory without the Axiom of Foundation we study the schema version of the principle of dependent choices in connection with Aczel's antifoundation axiom (a part of it), Boffa's anti-foundation axiom, and axiom of collection.

James sequences and Dependent Choices
✍ Marianne Morillon 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 240 KB

We prove James's sequential characterization of (compact) reflexivity in set-theory ZF + DC, where DC is the axiom of Dependent Choices. In turn, James's criterion implies that every infinite set is Dedekind-infinite, whence it is not provable in ZF. Our proof in ZF + DC of James' criterion leads us