Timeline for Incompleteness and nonstandard models of arithmetic
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2010 at 14:00 | comment | added | Marc Alcobé García | I realize I have mixed two things. I actually have no problem with Löwenheim-Skolem and the existence of elementarily equivalent models of PA with any cardinality. This is one reason for the existence of nonstandard models of arithmetic. But not the only reason. In the case of omega in ZFC, I didn't know about the ultrapower construction, but, as Bertrand Cody said, the first incompleteness theorem gives us an undecidable arithmetic statement, and hence a different reason: we then have different models that cannot be elementary equivalent. | |
| Jun 1, 2010 at 19:56 | vote | accept | Marc Alcobé García | ||
| Jun 1, 2010 at 19:56 | |||||
| Jun 1, 2010 at 17:36 | history | answered | Timothy Chow | CC BY-SA 2.5 |