## Journal of Symbolic Logic

### Admissible Suslin Cardinals in $L(\mathbf{R})$

Steve Jackson

#### Abstract

Assuming $\mathrm{AD} + (V = L(\mathbf{R}))$, it is shown that for $\kappa$ an admissible Suslin cardinal, $o(\kappa)$ (= the order type of the stationary subsets of $\kappa$) is "essentially" regular and closed under ultrapowers in a manner to be made precise. In particular, $o(\kappa) \gg \kappa^+, \kappa^{++}$, etc. It is conjectured that this characterizes admissibility for $L(\mathbf{R})$.

#### Article information

Source
J. Symbolic Logic, Volume 56, Issue 1 (1991), 260-275.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743565

Mathematical Reviews number (MathSciNet)
MR1131744

Zentralblatt MATH identifier
0729.03029

JSTOR
Jackson, Steve. Admissible Suslin Cardinals in $L(\mathbf{R})$. J. Symbolic Logic 56 (1991), no. 1, 260--275. https://projecteuclid.org/euclid.jsl/1183743565