## Journal of Symbolic Logic

### Countable Unions of Simple Sets in the Core Model

P. D. Welch

#### Abstract

We follow [8] in asking when a set of ordinals $X \subseteq \alpha$ is a countable union of sets in $K$, the core model. We show that, analogously to $L$, and $X$ closed under the canonical $\Sigma_1$ Skolem function for $K_\alpha$ can be so decomposed provided $K$ is such that no $\omega$-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erdos-type property.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 1 (1996), 293-312.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744941

Mathematical Reviews number (MathSciNet)
MR1380691

Zentralblatt MATH identifier
0863.03025

JSTOR