The Journal of Symbolic Logic

Research Article

A power function with a fixed finite gap everywhere

Carmi Merimovich

Computer Science Department, Tel-Aviv Academic College, 4 Antokolsky St., Tel-Aviv 64044, Israel, E-mail: carmi@mta.ac.il

Abstract

We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2 κ = κ +n together with 2 λ = λ +n for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible.

When κ remains an inaccessible, V κ is a model of ZFC satisfying 2 λ = λ +n for all cardinals λ.

(Received May 17 2000)

Key words and phrases

  • Forcing;
  • modified Radin forcing;
  • extender;
  • extender based forcing;
  • generalized continuum hypothesis;
  • singular cardinal hypothesis