Journal of Symbolic Logic

The Spectrum of Resplendency

John T. Baldwin

Abstract

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

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743319

Mathematical Reviews number (MathSciNet)
MR1056376

Zentralblatt MATH identifier
0699.03017

JSTOR

Citation

Baldwin, John T. The Spectrum of Resplendency. J. Symbolic Logic 55 (1990), no. 2, 626--636. https://projecteuclid.org/euclid.jsl/1183743319