## Journal of Symbolic Logic

### Locally Countable Models of $\Sigma_1$-Separation

Fred G. Abramson

#### Abstract

Let $\alpha$ be any countable admissible ordinal greater than $\omega$. There is a transitive set $A$ such that $A$ is admissible, locally countable, $On^A = \alpha$, and $A$ satisfies $\Sigma_1$-separation. In fact, if $B$ is any nonstandard model of $KP + \forall x \subseteq \omega$ (the hyperjump of $x$ exists), the ordinal standard part of $B$ is greater than $\omega$, and every standard ordinal in $B$ is countable in $B$, then $HC^B \cap$ (standard part of $B$) satisfies $\Sigma_1$-separation.

#### Article information

Source
J. Symbolic Logic, Volume 46, Issue 1 (1981), 96-100.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183740724

Mathematical Reviews number (MathSciNet)
MR604884

Zentralblatt MATH identifier
0481.03023

JSTOR
Abramson, Fred G. Locally Countable Models of $\Sigma_1$-Separation. J. Symbolic Logic 46 (1981), no. 1, 96--100. https://projecteuclid.org/euclid.jsl/1183740724