Timeline for How much of ZFC does Quine's New Foundations prove?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2010 at 15:18 | vote | accept | Amit Kumar Gupta | ||
| Nov 26, 2010 at 9:52 | comment | added | Rachid Atmai | New Foundations is just so weird. Just weaken extensionality to allow urelemente and it no longer proves infinity or the falsity of choice. It becomes consistent with choice and relatively consistent to ZFC. What is so special about atoms with NF that makes the theory so different? The other thing that always amazed me about stratification is that it succeeds in taking care of a whole bunch of paradoxes in the same way, namely by asserting that the universe is untyped. | |
| Nov 26, 2010 at 6:14 | comment | added | Andrés E. Caicedo | Yes, Pairing, power-set, union follow from stratified comprehension. Extensionality is an axiom. That choice is false is due to Specker: "The axiom of choice in Quine's new foundations for mathematical logic." Proceedings of the National Academy of Sciences of the USA 39, (1953) pp. 972-975. As a corollary, Infinity holds (suitably formulated, NF does not deal with Von Neumann ordinals; in NF, ordinals and cardinals are equivalence classes). Specker mentions in his paper another (silly) corollary, namely that GCH fails (as the proof that GCH implies choice can be formalized in NF). | |
| Nov 26, 2010 at 3:12 | comment | added | Rachid Atmai | New Foundations also proves the Power Set Axiom. The proof is in Halperin(1944). | |
| Nov 26, 2010 at 1:49 | history | answered | Andrés E. Caicedo | CC BY-SA 2.5 |