Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1

Downey, Rod; Jockusch, Carl G.

J. Symbolic Logic, Tome 64 (1999) no. 1, p. 45-52 / Harvested from Project Euclid

Résumé

We show that there is a computable Boolean algebra $\mathscr{B}$ and a computably enumerable ideal I of $\mathscr{B}$ such that the quotient algebra $\mathscr{B}/I$ is of Cantor-Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite Cantor-Bendixson rank.

Publié le : 1999-03-14
Classification:

@article{1183745690,
     author = {Downey, Rod and Jockusch, Carl G.},
     title = {Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 45-52},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745690}
}

Downey, Rod; Jockusch, Carl G. Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  45-52. http://gdmltest.u-ga.fr/item/1183745690/