Bulletin of Symbolic Logic

Turing computations on ordinals

Peter Koepke

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel's constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.

Article information

Bull. Symbolic Logic, Volume 11, Issue 3 (2005), 377-397.

First available in Project Euclid: 22 July 2005

Permanent link to this document

Digital Object Identifier

Zentralblatt MATH identifier


Koepke, Peter. Turing computations on ordinals. Bull. Symbolic Logic 11 (2005), no. 3, 377--397. doi:10.2178/bsl/1122038993. https://projecteuclid.org/euclid.bsl/1122038993

Export citation