Minimality of non-σ-scattered orders

Tetsuya Ishiu, and Justin Tatch Moore. "Minimality of non-σ-scattered orders." Fundamenta Mathematicae 205.1 (2009): 29-44. <http://eudml.org/doc/282590>.

@article{TetsuyaIshiu2009,
abstract = {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.},
author = {Tetsuya Ishiu, Justin Tatch Moore},
journal = {Fundamenta Mathematicae},
keywords = {Aronszajn line; Specker type; real type; Countryman type; -scattered linear order; Proper Forcing Axiom},
language = {eng},
number = {1},
pages = {29-44},
title = {Minimality of non-σ-scattered orders},
url = {http://eudml.org/doc/282590},
volume = {205},
year = {2009},
}

TY - JOUR
AU - Tetsuya Ishiu
AU - Justin Tatch Moore
TI - Minimality of non-σ-scattered orders
JO - Fundamenta Mathematicae
PY - 2009
VL - 205
IS - 1
SP - 29
EP - 44
AB - 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.
LA - eng
KW - Aronszajn line; Specker type; real type; Countryman type; -scattered linear order; Proper Forcing Axiom
UR - http://eudml.org/doc/282590
ER -