Strict independence

Itay Kaplan, Alexander Usvyatsov

Research output: Contribution to journalArticlepeer-review


We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular, it follows from our investigation that in resilient theories strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing. We prove simple characterizations of such sequences in resilient theories, as well as of Morley sequences which are witnesses. As a by-product we obtain information on types co-dominated by generically stable types in dependent theories. For example, we prove that every Morley sequence in such a type is a witness.

Original languageEnglish
Article number1450008
JournalJournal of Mathematical Logic
Issue number2
StatePublished - 13 Dec 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 World Scientific Publishing Company.


  • Strict independence
  • dependent theories
  • forking
  • resilient theories
  • weight


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