Definability of initial segments
| dc.creator | Shelah, Saharon | |
| dc.creator | Tsuboi, Akito | |
| dc.date | 2001-04-28 | |
| dc.date.accessioned | 2026-07-07T04:41:31Z | |
| dc.date.available | 2026-07-07T04:41:31Z | |
| dc.description | We consider implicit definability of the standard part {0,1,...} in nonstandard models of Peano arithmetic (PA), and we ask whether there is a model of PA in which the standard part is implicitly definable. In section 1, we define a certain class of formulas, and show that in any model of PA the standard part is not implicitly defined by using such formulas. In section 2 we construct a model of PA in which the standard part is implicitly defined. To construct such a model, first we assume a set theoretic hypothesis diamondsuit_{S_lambda^{lambda^+}}, which is an assertion of the existence of a very general set. Then we shall eliminate the hypothesis using absoluteness for the existence of a model having a tree structure with a certain property. | |
| dc.identifier | https://arxiv.org/abs/math/0104277 | |
| dc.identifier | http://arxiv.org/abs/math/0104277 | |
| dc.identifier | Notre Dame J. Formal Logic 43 No. 2 (2002) 65--73 (2003) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61391 | |
| dc.subject | Logic | |
| dc.title | Definability of initial segments | |
| dc.type | text |