Categoricity of theories in \(L_{\kappa^*,\omega}\), when \(\kappa^*\) is a measurable cardinal. II (Q2773244)

In this `Part II' [for Part I see \textit{S. Shelah} and \textit{O. Kolman}, ibid. 151, No. 3, 209-240 (1996; Zbl 0882.03039)], the author establishes the categoricity result of a theory in \(L_{\kappa,\omega}\), with measurable \(\kappa\). (`Part I' was about the amalgamation property.) For this review, let \(\tau:= \kappa+|T|\), where \(T\) is the theory in question, and \(\nu:= \beth_{(2^\tau)^+}\).NEWLINENEWLINENEWLINEThe theorem reads: If \(T\) is categorical at a successor cardinal \(\lambda> \nu\), then \(T\) is categorical at every \(\mu\) between \(\nu\) and \(\lambda\), i.e. \(\nu\leq \mu<\lambda\).NEWLINENEWLINENEWLINEOf course, this is only a crude ``sub-head-line'' of ardurous work on the analysis of types, of forking, and of constructions of nonisomorphic models. The theorem itself is sharpened by considering \(\mu\) outside of the above range.