On interpretations of bounded arithmetic and bounded set theory
| dc.creator | Pettigrew, Richard | |
| dc.date | 2008-07-30 | |
| dc.date | 2008-08-17 | |
| dc.date.accessioned | 2026-07-07T09:56:45Z | |
| dc.date.available | 2026-07-07T09:56:45Z | |
| dc.description | In a recent paper, Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic. THEOREM: The first-order theories of Peano arithmetic and ZF with the axiom of infinity negated are bi-interpretable: that is, they are mutually interpretable with interpretations that are inverse to each other. In this note, I describe a theory of sets that stands in the same relation to the bounded arithmetic IDelta0 + exp. Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's interpretation of arithmetic in set theory. Instead, I am forced to produce a different interpretation. | |
| dc.description | 12 pages; section on omega-models removed due to error; references added and typos corrected | |
| dc.identifier | https://arxiv.org/abs/0807.4850 | |
| dc.identifier | http://arxiv.org/abs/0807.4850 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167089 | |
| dc.subject | Logic | |
| dc.subject | 03C62 | |
| dc.title | On interpretations of bounded arithmetic and bounded set theory | |
| dc.type | text |