We introduce the notion of an invariantly universal pair (S;E) where S is an analytic quasi-order and E \subseteq S is an analytic equivalence relation. This means that for any analytic quasi-order R there is a Borel set B invariant under E such that R is Borel bireducible with the restriction of S to B. We prove a general result giving a sucient condition for invariant universality, and we demonstrate several applications of this theorem by showing that the phenomenon of invariant universality is widespread. In fact it occurs for a great number of complete analytic quasi-orders, arising in dierent areas of mathematics, when they are paired with natural equivalence relations.

Invariantly universal analytic quasi-orders

MOTTO ROS, Luca
2013-01-01

Abstract

We introduce the notion of an invariantly universal pair (S;E) where S is an analytic quasi-order and E \subseteq S is an analytic equivalence relation. This means that for any analytic quasi-order R there is a Borel set B invariant under E such that R is Borel bireducible with the restriction of S to B. We prove a general result giving a sucient condition for invariant universality, and we demonstrate several applications of this theorem by showing that the phenomenon of invariant universality is widespread. In fact it occurs for a great number of complete analytic quasi-orders, arising in dierent areas of mathematics, when they are paired with natural equivalence relations.
2013
365
4
1901
1931
http://arxiv.org/pdf/1003.4932v2
Analytic equivalence relations; analytic quasi-orders; Borel reducibility; completeness; invariant universality; colored linear orders; dendrites; (ultrametric) Polish spaces; separable Banach spaces
CAMERLO R; MARCONE A; MOTTO ROS L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/148726
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