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EnglishWe 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: | |
| Data di pubblicazione: | 2013 |
| Rivista: | |
| 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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