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Summer 1986 A non structure theorem for an infinitary theory which has the unsuperstability property
Rami Grossberg, Saharon Shelah
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Illinois J. Math. 30(2): 364-390 (Summer 1986). DOI: 10.1215/ijm/1256044645

Abstract

Let $\kappa$, $\lambda$ be infinite cardinals, $\psi \in L_{\kappa^{+},\omega}$. We say that the sentence $\psi$ has the $\lambda$-unsuperstability property if there are $\{\varphi_{n}(\bar{\mathbf{x}},\bar{\mathbf{y}}): n < \omega\}$ quantifier free first order formulas in $L$, a model $M$ of $\psi$, and there exist $\{\bar{\mathbf{a}}_{\eta}: \eta \in^{\omega \geq} \lambda\} \subseteq |M|$ such that for all $\eta \in^{\omega}\lambda$, and for every $\nu \in^{\omega >}\lambda$, $$\nu < \eta \Leftrightarrow M \vDash \varphi_{l(\nu)}[\bar{\mathbf{a}}_{\nu},\bar{\mathbf{a}}_{\eta}].$$

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Rami Grossberg. Saharon Shelah. "A non structure theorem for an infinitary theory which has the unsuperstability property." Illinois J. Math. 30 (2) 364 - 390, Summer 1986. https://doi.org/10.1215/ijm/1256044645

Information

Published: Summer 1986
First available in Project Euclid: 20 October 2009

zbMATH: 0578.03020
MathSciNet: MR840135
Digital Object Identifier: 10.1215/ijm/1256044645

Subjects:
Primary: 03C45

Rights: Copyright © 1986 University of Illinois at Urbana-Champaign

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Vol.30 • No. 2 • Summer 1986
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