Timeline for A question about sentences undecidable in Peano's Arithmetic
Current License: CC BY-SA 3.0
6 events
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Jul 26, 2015 at 18:31 | comment | added | Garabed Gulbenkian | I am really trying to avoid theories in which second order axioms are "represented | |
Jul 25, 2015 at 17:32 | comment | added | Garabed Gulbenkian | The question at the end of my previous comment is not quite what I meant to ask. I meant to ask whether every consistent and axiomatizable extension of PA-even if based upon higher order logic-has non-standard models which contain "infinite" positive integers. I am not too sure about exactly what Godel's incompleteness theorem and model theory have to say regarding consistent and axiomatizable extensions of PA that are not based upon first order logic. | |
Jul 24, 2015 at 18:09 | comment | added | Garabed Gulbenkian | Many thanks for your answers which have given me alot to think about. I thought that Hilbert and Bernays presented the first formalized and axiomatizable version of what I call SOA. You do not mention whether any of the interesting examples of sentences such as the Paris-Harrington theorem or Goodstein's theorem-which have been shown to be undecidable in PA-are also undecidable in SOA. Finally, does every axiomatizable theory-even if based upon higher order logic-have non-standard models which contain "infinite" positive integers? | |
Jul 24, 2015 at 16:35 | comment | added | Noah Schweber | This is mostly true, but the last paragraph is wrong: TA has lots of nonstandard countable models. | |
Jul 24, 2015 at 12:46 | review | First posts | |||
Jul 24, 2015 at 13:18 | |||||
Jul 24, 2015 at 12:42 | history | answered | none | CC BY-SA 3.0 |