Year: 2013
Type: preprint
Abstract: We exposit two previously unpublished theorems of Leo Harrington. The first theorem says that there exist arithmetical singletons which are arithmetically incomparable. The second theorem says that there exists a ranked point which is not an arithmetical singleton. Unlike Harrington's proofs of these theorems, our proofs do not use the finite- or infinite-injury priority method. Instead they use an oracle construction adapted from the standard proof of the Friedberg Jump Theorem.
Source: arXiv (Cornell University)
Author: Simpson, Stephen G.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1577765283