This article is cited in 5 papers

Ideals without minimal elements in Rogers semilattices

A. A. Issakhov

Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Alma-Ata, 050038, Kazakhstan

Abstract: We prove a criterion for the existence of a minimal numbering, which is reducible to a given numbering of an arbitrary set. The criterion is used to show that, for any infinite $A$-computable family $F$ of total functions, where $\varnothing'\le_TA$, the Rogers semilattice $\mathcal R_A(F)$ of $A$-computable numberings for $F$ contains an ideal without minimal elements.

Keywords: minimal numbering, $A$-computable numbering, Rogers semilattice, ideal.

UDC: 510.54

Received: 06.11.2014

DOI: 10.17377/alglog.2015.54.301

 English version: Algebra and Logic, 2015, 54:3, 197–203

Bibliographic databases:

• 
• 
•