Skip to main content
eScholarship
Open Access Publications from the University of California

On the number of dedekind cuts and two-cardinal models of dependent theories

  • Author(s): Chernikov, A
  • Shelah, S
  • et al.
Abstract

© Cambridge University Press 2015. For an infinite cardinal κ, let ded κ denote the supremum of the number of Dedekind cuts in linear orders of size κ. It is known that κ < ded κ ≤2κfor all κ and that ded κ < 2κis consistent for any κ of uncountable cofinality. We prove however that 2κ≤ ded(ded(ded(ded κ))) always holds. Using this result we calculate the Hanf numbers for the existence of two-cardinal models with arbitrarily large gaps and for the existence of arbitrarily large models omitting a type in the class of countable dependent first-order theories. Specifically, we show that these bounds are as large as in the class of all countable theories.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View