Infinite Time Turing Machines
| dc.creator | Hamkins, Joel David | |
| dc.creator | Lewis, Andy | |
| dc.date | 1998-08-21 | |
| dc.date.accessioned | 2026-07-07T05:25:46Z | |
| dc.date.available | 2026-07-07T05:25:46Z | |
| dc.description | We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of computation on the reals and concepts of decidability and semi-decidability for sets of reals as well as individual reals. Every Pi^1_1 set, for example, is decidable by such machines, and the semi-decidable sets form a portion of the Delta^1_2 sets. Our oracle concept leads to a notion of relative computability for reals and sets of reals and a rich degree structure, stratified by two natural jump operators. | |
| dc.description | 57 pages, 4 figures, to appear in the Journal of Symbolic Logic | |
| dc.identifier | https://arxiv.org/abs/math/9808093 | |
| dc.identifier | http://arxiv.org/abs/math/9808093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77307 | |
| dc.subject | Logic | |
| dc.subject | 03D30; 03D60 | |
| dc.title | Infinite Time Turing Machines | |
| dc.type | text |