From well to better, the space of ideals

• Autorzy: Raphaël Carroy , Yann Pequignot
• Języki publikacji: EN

Abstrakty

EN

On the one hand, the ideals of a well quasi-order (wqo) naturally form a compact topological space into which the wqo embeds. On the other hand, Nash-Williams' barriers are given a uniform structure by embedding them into the Cantor space.
We prove that every map from a barrier into a wqo restricts on a barrier to a uniformly continuous map, and therefore extends to a continuous map from a countable closed subset of the Cantor space into the space of ideals of the wqo. We then prove that, by shrinking further, any such continuous map admits a canonical form with regard to the points whose image is not isolated. cr As a consequence, we obtain a simple proof of a result on better quasi-orders (bqo); namely, a wqo whose set of non-principal ideals is a bqo is actually a bqo.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 05D10: Ramsey theory
• 03E75: Applications of set theory
• 06A06: Partial order, general
• 06A07: Combinatorics of partially ordered sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 227
• Numer: 3
• Strony: 247-270

Daty

wydano

2014

Twórcy

autor

Raphaël Carroy

• Dipartimento di Matematica "Giuseppe Peano", Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

autor

Yann Pequignot

• Institut des systèmes d'information, Quartier UNIL-Dorigny, Bâtiment Internef, CH-1015 Lausanne, Switzerland
• Université Paris 7, Paris, France

Identyfikatory

DOI

10.4064/fm227-3-2