Invariantly universal analytic quasi-orders

Camerlo, Riccardo; Marcone, A.; Motto Ros, L.

doi:10.1090/S0002-9947-2012-05618-2

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We introduce the notion of an invariantly universal pair (S,E) where S is an analytic quasi-order and E ⊆ 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 sufficient 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 different areas of mathematics, when they are paired with natural equivalence relations.

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Titolo:	Invariantly universal analytic quasi-orders
Autori:	CAMERLO, RICCARDO A. Marcone L. Motto Ros mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2013
Rivista:	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Abstract:	We introduce the notion of an invariantly universal pair (S,E) where S is an analytic quasi-order and E ⊆ 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 sufficient 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 different areas of mathematics, when they are paired with natural equivalence relations.
Handle:	http://hdl.handle.net/11567/948944
Appare nelle tipologie:	01.01 - Articolo su rivista

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