Theories of Rogers Semilattices of Analytical Numberings

2021

Closed access Metadata (CSL-JSON)
DOI 10.1134/s1995080221040065
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

The paper studies Rogers semilattices, i.e. upper semilattices induced by the reducibility between numberings. Under the assumption of Projective Determinacy, we prove that for every non-zero natural number $$n$$ , there are infinitely many pairwise elementarily non-equivalent Rogers semilattices for $$\Sigma^{1}_{n}$$ -computable families.