Addendum to: A Survey of Mu\vcnik and Medvedev Degrees
Peter Hinman
TL;DR
This paper provides additional material and a proof related to the structure of strong degrees, specifically showing an initial segment with dual theory IPC, expanding on previous survey work in the field.
Contribution
It presents new proofs and material that were omitted from the original survey of Mučnik and Medvedev degrees, enhancing understanding of their structure.
Findings
Existence of an initial segment with dual theory IPC
New proof of Theorem K
Additional structural insights into strong degrees
Abstract
We include here some material that did not make its way into the published version (Bull. Symb. Log 18-2, June 2012, pp. 161-229, arXiv:1007.2376), in particular a proof of Theorem K to the effect that there is an initial segment of the strong degrees with dual theory IPC, the intuitionistic propositional calculus.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Algorithms and Data Compression · Numerical Methods and Algorithms