Journal of Symbolic Logic

Undefinability of $\kappa$-Well-Orderings in $L_{\infty\kappa}$

Juha Oikkonen

Abstract

We prove that the class of trees with no branches of cardinality $\geq\kappa$ is not RPC definable in $L_{\infty\kappa}$ when $\kappa$ is regular. Earlier such a result was known for $L_{\kappa^+\kappa}$ under the assumption $\kappa^{<\kappa} = \kappa$. Our main result is actually proved in a stronger form which covers also $L_{\infty\lambda}$ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality $\kappa$.

Article information

Source
J. Symbolic Logic, Volume 62, Issue 3 (1997), 999-1020.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745309

Mathematical Reviews number (MathSciNet)
MR1472135

Zentralblatt MATH identifier
0894.03014

JSTOR
Oikkonen, Juha. Undefinability of $\kappa$-Well-Orderings in $L_{\infty\kappa}$. J. Symbolic Logic 62 (1997), no. 3, 999--1020. https://projecteuclid.org/euclid.jsl/1183745309