Timeline for Are there any natural recursively but not primitive-recursively axiomatized theories?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2015 at 11:13 | comment | added | Thomas Benjamin | JDH: Since Lindenbaum algebras define $\forall$ as infinite conjunctions and $\exists$ as infinite disjunctions, what happens to the undecidable theory $T$ in question when such infinite conjunctions and disjunctions are removed and only finite conjunctions and disjunctions remain (bounded quantification)? If I understand correctly, all terms in the conjunctions and disjunctions are variable-free. Does this make this fragment of $T$ 'contentual' ('finitary' in Hilbert's terminology) and is this fragment always decidable? | |
| Jul 3, 2012 at 18:31 | comment | added | Peter Smith | My comment, on reflection, is the same as for Ali Enayat's lovely case. Here too we have an r.e. set of sentences, but not recursively decidable as presented, so not a recursively axiomatized theory in the (I hope non-deviant) sense I was using. No? | |
| Jun 29, 2012 at 21:24 | vote | accept | Peter Smith | ||
| Jun 30, 2012 at 22:37 | |||||
| Jun 29, 2012 at 17:07 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |