Timeline for 4-quantifier formula not decided by ZF
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 3 at 11:41 | comment | added | Pedro Sánchez Terraf | @ChristopherKing Farmer is correct, I meant the total count of quantifiers (bounded or otherwise). | |
| Dec 3 at 0:19 | comment | added | Farmer S | I believe it is total quantifiers, including bounded. (I believe things are referring back to Harvey Friedman's FOM post linked by Timothy Chow above. In the original question, the linked question "This interesting question" cites the paper by Kurt Maes, which cites the post "196:Quantifier complexity in set theory" by Harvey Friedman, but the link provided in the paper for Friedman's post seems to be in error, as it goes to something else.) | |
| Dec 2 at 19:07 | comment | added | James E Hanson | In addition to Christopher's question, are we counting bounded quantifiers as quantifiers? | |
| Dec 2 at 16:41 | comment | added | Christopher King | Total number of quantifiers, or quantifier alternations? | |
| Dec 2 at 13:35 | comment | added | Timothy Chow | Back in 2003, Harvey Friedman wrote on the FOM list, "I conjecture that every 4 quantifier sentence is decided in a somewhat weak fragment of ZF (it has to include the power set axiom)." So apparently the question was open back then. Admittedly, that was a rather long time ago, and for example it (just barely) predates the work of Kurt Maes showing that AC can be expressed using 5 quantifiers. | |
| Dec 2 at 13:12 | history | asked | Pedro Sánchez Terraf | CC BY-SA 4.0 |