Homogeneous tree
id:
homogeneous-tree-259-1644650
title:
Homogeneous tree
text:
In descriptive set theory, a tree over a product set Y × Z is said to be homogeneous if there is a system of measures ⟨ μ s ∣ s ∈ < ω Y ⟩ such that the following conditions hold: μ s is a countably-additive measure on { t ∣ ⟨ s , t ⟩ ∈ T } .
The measures are in some sense compatible under restriction of sequences: if s 1 ⊆ s 2 , then μ s 1 = 1 ⟺ μ s 2 = 1 .
If x is in the projection of T , the ultrapower by ⟨ μ x ↾ n ∣ n ∈ ω ⟩ is wellfounded. An equivalent definition is produced when the final c
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wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Homogeneous_tree
date created:
date modified:
2024-03-04T06:19:59Z
main entity:
{"identifier":"Q5891336","url":"https://www.wikidata.org/entity/Q5891336"}
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fields total:
13
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13