The Recursion Theorem and Infinite Sequences
| dc.creator | Miller, Arnold W. | |
| dc.date | 2008-01-14 | |
| dc.date.accessioned | 2026-07-07T08:54:21Z | |
| dc.date.available | 2026-07-07T08:54:21Z | |
| dc.description | In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove that there exists an increasing sequence such that W_{e_n}={e_{n+1},e_{n+2},...} for every n. We call a nonempty computably enumerable set A self-constructing if W_e=A for every e in A. We show that every nonempty computable enumerable set which is disjoint from an infinite computable set is one-one equivalent to a self-constructing set | |
| dc.identifier | https://arxiv.org/abs/0801.2097 | |
| dc.identifier | http://arxiv.org/abs/0801.2097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145898 | |
| dc.subject | Logic | |
| dc.subject | 03E25; 03E99 | |
| dc.title | The Recursion Theorem and Infinite Sequences | |
| dc.type | text |