Journal of Symbolic Logic

The Spectrum of Resplendency

John T. Baldwin

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


Let $T$ be a complete countable first order theory and $\lambda$ an uncountable cardinal. Theorem 1. If $T$ is not superstable, $T$ has $2^\lambda$ resplendent models of power $\lambda$. Theorem 2. If $T$ is strictly superstable, then $T$ has at least $\min(2^\lambda,\beth_2)$ resplendent models of power $\lambda$. Theorem 3. If $T$ is not superstable or is small and strictly superstable, then every resplendent homogeneous model of $T$ is saturated. Theorem 4 (with Knight). For each $\mu \in \omega \cup \{\omega, 2^\omega\}$ there is a recursive theory in a finite language which has $\mu$ resplendent models of power $\kappa$ for every infinite $\kappa$.

Article information

J. Symbolic Logic, Volume 55, Issue 2 (1990), 626-636.

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Baldwin, John T. The Spectrum of Resplendency. J. Symbolic Logic 55 (1990), no. 2, 626--636.

Export citation