## Journal of Symbolic Logic

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

Klaus Sutner

#### 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

https://projecteuclid.org/euclid.jsl/1183743314

Mathematical Reviews number (MathSciNet)
MR1056371

Zentralblatt MATH identifier
0705.03026

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