This article is cited in 1 paper

Minimal Elements and Minimal Covers in Rogers Semilattice of Computable Numberings in Hyperarithmetical Hierarchy

N. A. Baklanova

Novosibirsk State University

Abstract: Proved that Rogers semilattice of any infinite $\Sigma_{\omega}$-computable family contains infinitely many minimal elements, and each non-$0'$-universal numbering has infinitely many minimal covers.

Keywords: numbering, Rogers semilattice, hyperarithmetical hierarchy, minimal elements, minimal covers.

UDC: 510.5

Received: 25.02.2011