کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4662143 1633516 2009 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Ordinal machines and admissible recursion theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
Ordinal machines and admissible recursion theory
چکیده انگلیسی

We generalize standard Turing machines, which work in time ω on a tape of length ω, to α-machines with time α and tape length α, for α some limit ordinal. We show that this provides a simple machine model adequate for classical admissible recursion theory as developed by G. Sacks and his school. For α an admissible ordinal, the basic notions of α-recursive or α-recursively enumerable are equivalent to being computable or computably enumerable by an α-machine, respectively. We emphasize the algorithmic approach to admissible recursion theory by indicating how the proof of the Sacks–Simpson theorem, i.e., the solution of Post’s problem in α-recursion theory, could be based on α-machines, without involving constructibility theory.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 160, Issue 3, September 2009, Pages 310-318