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.

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 λ2 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 μ2 LS(K)\mu\geq|2^{LS(K)}|.

Revised on August 4, 2012 19:20:35 by Zoran Škoda (95.168.113.34)