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.
Invariantly universal analytic quasi-orders / Camerlo, Riccardo; A., Marcone; L., Motto Ros. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 365:4(2013), pp. 1901-1931. [10.1090/S0002-9947-2012-05618-2]
Invariantly universal analytic quasi-orders
CAMERLO, RICCARDO;
2013
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.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2503542
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