Minimality of non-σ-scattered orders

• Autorzy: Tetsuya Ishiu , Justin Tatch Moore
• Języki publikacji: EN

Abstrakty

EN

We will characterize-under appropriate axiomatic assumptions-when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA⁺, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative consistency of: There are no minimal non-σ-scattered linear orders. In the process of establishing these results, we will prove combinatorial characterizations of when a given linear order is σ-scattered and when it contains either a real or Aronszajn type.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E75: Applications of set theory
• 06A05: Total order

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 205
• Numer: 1
• Strony: 29-44

Daty

wydano

2009

Twórcy

autor

Tetsuya Ishiu

• Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.

autor

Justin Tatch Moore

• Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, U.S.A.

Identyfikatory

DOI

10.4064/fm205-1-2