Journal of Symbolic Logic

The Ordertype of $\beta$-R.E. Sets

Klaus Sutner

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Abstract

Let $\beta$ be an arbitrary limit ordinal. A $\beta$-r.e. set is $l$-finite iff all its $\beta$-r.e. subsets are $\beta$-recursive. The $l$-finite sets correspond to the ideal of finite sets in the lattice of r.e. sets. We give a characterization of $l$-finite sets in terms of their ordertype: a $\beta$-r.e. set is $l$-finite iff it has ordertype less than $\beta^\ast$, the $\Sigma_1$ projectum of $\beta$.

Article information

Source
J. Symbolic Logic, Volume 55, Issue 2 (1990), 573-576.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743314

Mathematical Reviews number (MathSciNet)
MR1056371

Zentralblatt MATH identifier
0705.03026

JSTOR
links.jstor.org

Citation

Sutner, Klaus. The Ordertype of $\beta$-R.E. Sets. J. Symbolic Logic 55 (1990), no. 2, 573--576. https://projecteuclid.org/euclid.jsl/1183743314


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