Examples in dependent theories

Itay Kaplan, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In the first part we show a counterexample to a conjecture by Shelah regarding the existence of indiscernible sequences in dependent theories (up to the first inaccessible cardinal). In the second part we discuss generic pairs, and give an example where the pair is not dependent. Then we define the notion of directionality which deals with counting the number of coheirs of a type and we give examples of the different possibilities. Then we discuss nonsplintering, an interesting notion that appears in the work of Rami Grossberg, Andrés Villaveces andMonica VanDieren, and we show that it is not trivial (in the sense that it can be different than splitting) whenever the directionality of the theory is not small. In the appendix we study dense types in RCF.

Original languageAmerican English
Pages (from-to)585-619
Number of pages35
JournalJournal of Symbolic Logic
Volume79
Issue number2
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014, Association for Symbolic Logic.

Keywords

  • Dense types
  • Dependent theories
  • Directionality
  • Generic pair
  • Indiscernible sequences
  • Model theory
  • NIP
  • Splintering

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