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 TT be a countable theory in L ω 1,ωL_{\omega_1,\omega} (cf. infinitary logic). If there exists λ ω 1\lambda\geq\beth_{\omega_1} such that the number of isomorphism classes of models in cardinality λ\lambda is I(λ,T)=1I(\lambda,T) = 1 then I(μ,T)=1I(\mu,T) = 1 holds for every μ ω 1\mu\geq\beth_{\omega_1}. More generally, let K=(K,<)K = (K,\lt) be an abstract elementary class. If there exists λ|2 LS(K)|\lambda\geq|2^{LS(K)}| such that the number of isomorphism classes of models in cardinality λ\lambda is I(λ,K)=1I(\lambda,K) = 1 then I(μ,K)=1I(\mu,K) = 1 holds for every μ|2 LS(K)|\mu\geq|2^{LS(K)}|.

Revised on February 15, 2015 03:06:05 by Todd Trimble (67.81.95.215)