Timeline for Incompleteness and nonstandard models of arithmetic
Current License: CC BY-SA 2.5
2 events
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| Jun 15, 2010 at 11:35 | comment | added | Carl Mummert | With second-order semantics, we have to distinguish between syntactic completeness and semantic completeness, because these are no longer the same. Being categorical is stronger than being semantically complete, and PA with second-order induction is semantically complete. No effective theory with equality in 2nd-order logic with an infinite model is syntactically complete, so the fact that PA with second-order semantics is not syntactically complete is not really its fault. That is: it's not usually interesting to ask whether a 2nd-order theory is syntactically complete, because it isn't. | |
| Jun 6, 2010 at 14:51 | history | answered | Jeremy Shipley | CC BY-SA 2.5 |