Erratum
Erratum to “Categoricity in abstract elementary classes with no maximal models” [Ann. Pure Appl. Logic 141 (2006) 108–147]

https://doi.org/10.1016/j.apal.2012.09.003
Under an Elsevier user license
open archive

Abstract

In the paper “Categoricity in abstract elementary classes with no maximal models”, we address gaps in Saharon Shelah and Andrés Villavecesʼ (1999) proof in [4] of the uniqueness of limit models of cardinality μ in λ-categorical abstract elementary classes with no maximal models, where λ is some cardinal larger than μ. Both [4] (Shelah and Villaveces, 1999) and [5] (VanDieren, 2006) employ set theoretic assumptions, namely GCH and Φμ+(Scf(μ)μ+).

Recently, Tapani Hyttinen pointed out a problem in an early draft of [3] (Grossberg et al., 2011) to Villaveces. This problem stems from the proof in Shelah and Villavecesʼ (1999) [4] that reduced towers are continuous. Residues of this problem also infect the proof of Proposition II.7.2 in VanDieren (2006) [5]. We respond to the issues in Shelah and Villaveces (1999) [4] and VanDieren (2006) [5] with alternative proofs under the strengthened assumption that the abstract elementary class is categorical in μ+.

Cited by (0)

1

The author was partially sponsored for this work by grant DMS 0801313 of the National Science Foundation.