The Ordertype of $\beta$-R.E. Sets
Sutner, Klaus
J. Symbolic Logic, Tome 55 (1990) no. 1, p. 573-576 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 $\beta$.
Publié le : 1990-06-14
Classification:  
@article{1183743314,
     author = {Sutner, Klaus},
     title = {The Ordertype of $\beta$-R.E. Sets},
     journal = {J. Symbolic Logic},
     volume = {55},
     number = {1},
     year = {1990},
     pages = { 573-576},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743314}
}

Sutner, Klaus. The Ordertype of $\beta$-R.E. Sets. J. Symbolic Logic, Tome 55 (1990) no. 1, pp.  573-576. http://gdmltest.u-ga.fr/item/1183743314/