- Regular Ultrapowers at Regular Cardinals
- Notre Dame Journal of Formal Logic
- Volume | Issue number
- 56 | 3
- Pages (from-to)
- Number of pages
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
In earlier work by the first and second authors, the equivalence of a finite square principle □ finλD with various model-theoretic properties of structures of size λ and regular ultrafilters was established. In this paper we investigate the principle □ finλD -and thereby the above model-theoretic properties-at a regular cardinal. By Chang's two-cardinal theorem, □ finλD holds at regular cardinals for all regular filters D if we assume the generalized continuum hypothesis (GCH). In this paper we prove in ZFC that, for certain regular filters that we call doubly+ regular, □ finλD holds at regular cardinals, with no assumption about GCH. Thus we get new positive answers in ZFC to Open Problems 18 and 19 in Chang and Keisler's book Model Theory.
- go to publisher's site
- Accepted author manuscript
- Other links
- Link to publication in Scopus
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.