Timeline for Naturally definable sets of natural numbers
Current License: CC BY-SA 2.5
4 events
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| Feb 3, 2010 at 20:06 | comment | added | Joel David Hamkins | I guess the argument in my third point was assuming that by subformula you meant 'proper subformula'. It wouldn't apply to a formula phi(x) which was itself equivalent to "x=1", say. (for example, you could consider the whole formula on the right hand side). So the third point should say, if Con(PA), then every formula not equivalent to "x=n" is natural. | |
| Feb 3, 2010 at 20:00 | comment | added | Hans-Peter Stricker | By the way: your third observation is exactly the kind of simple argument I had in mind in my Question #1a. | |
| Feb 3, 2010 at 19:55 | comment | added | Hans-Peter Stricker | You are perfectly right with your third observation that phi(x) is equivalent to exists y ( y=x and phi(y)) which by my definiton is natural. I guess I could manage to circumvent this prestidigitation. But Reid's answer has discouraged me even more, so I'm going to give up this maybe too crude idea of "naturalness" (even though my intuition protests). | |
| Feb 3, 2010 at 19:39 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |