Infinite Time Turing Machines
逻辑
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/9808093,
title = {Infinite Time Turing Machines},
author = {Joel David Hamkins and Andy Lewis},
journal= {arXiv preprint arXiv:math/9808093},
year = {2007}
}
备注
57 pages, 4 figures, to appear in the Journal of Symbolic Logic