# nLab Saharon Shelah

Saharon Shelah is a leading model theorist. He developed the classification theory, introduced stability theory, abstract elementary classes, and Galois types in particular. He is also the creator of pcf theory?, among other things.

Shelah’s articles are numerated and often referred to according to this numeration.

Shelah’s categoricity conjecture. Let $T$ be a countable theory in $L_{\omega_1,\omega}$ (cf. infinitary logic). If there exists $\lambda\geq\beth_{\omega_1}$ such that the number of isomorphism classes of models in cardinality $\lambda$ is $I(\lambda,T) = 1$ then $I(\mu,T) = 1$ holds for every $\mu\geq\beth_{\omega_1}$. More generally, let $K = (K,\lt)$ be an abstract elementary class. If there exists $\lambda\geq|2^{LS(K)}|$ such that the number of isomorphism classes of models in cardinality $\lambda$ is $I(\lambda,K) = 1$ then $I(\mu,K) = 1$ holds for every $\mu\geq|2^{LS(K)}|$.

Revised on February 18, 2016 19:44:56 by Todd Trimble (67.81.95.215)