Abstract

If α is a singular cardinal (either real or fake) in L, I exhibit many natural α-re subsets, defined uniformly from the ▵ 1 subsets of α. If α is a true cardinal this provides an uppersemilattice (usl) embedding from the lattice of ▵ 1 subsets of α into the usl of α-re-degrees. It will also be shown that this embedding cannot be extended to the Σ 1 subsets of α