Timeline for FOL->ZF->HOL (Interpretation)
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Nov 13, 2010 at 18:37 | history | edited | Bubba88 | CC BY-SA 2.5 |
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| Nov 11, 2010 at 20:19 | vote | accept | Bubba88 | ||
| Nov 11, 2010 at 12:41 | comment | added | Carl Mummert | @Bubba: the simplest way is, as you say, to just interpret the higher-order quantifiers in set theory. The reason that people sometimes say that HOL has more expressive power than FOL is because they are thinking of working in the same language, just changing the allowable quantifiers. For example, the second-order theory of groups includes set quantifiers, while the first-order theory of groups does not. But the first-order theory of ZFC is expressive enough to state every sentence from the second-order theory of groups. | |
| Nov 11, 2010 at 12:01 | answer | added | Joel David Hamkins | timeline score: 3 | |
| Nov 11, 2010 at 11:09 | comment | added | Bubba88 | If there is a direct method of encoding HOLs in FOL, I would be glad to see it | |
| Nov 11, 2010 at 11:09 | history | asked | Bubba88 | CC BY-SA 2.5 |