A dichotomy theorem for regular types

Ehud Hrushovski*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Theorem 1.(a) LetT be a superstable theory without the omitting type order property. Then every regular type is either locally modular, or non-orthogonal to a strongly regular type. In the latter case, a realization of the strongly regular type can be found algebraically in any realization of the given one.(b) LetT be a superstable theory with NOTOP and NDOP. Then every regular type is either locally modular or strongly regular.Theorem 2.(a) Letp be a nontrivial regular type. Thenp-weight is continuous and definable inside some definable setD of positivep-weight. Ifp is non-orthogonal toB, thenD can be chosen definable overB.(b) Letp be a nontrivial regular type of depth 0. Let stp(a/B) bep-semi-regular. Thena lies in some acl(B)-definable setD such thatp-weight is continuousand definable insideD.

Original languageEnglish
Pages (from-to)157-169
Number of pages13
JournalAnnals of Pure and Applied Logic
Volume45
Issue number2 PART 1
DOIs
StatePublished - 12 Dec 1989

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