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Homogeneous tree : ウィキペディア英語版 | Homogeneous tree In descriptive set theory, a tree over a product set is said to be homogeneous if there is a system of measures . * The measures are in some sense compatible under restriction of sequences: if , then . * If is in the projection of , the ultrapower by is wellfounded. An equivalent definition is produced when the final condition is replaced with the following: * There are such that . This condition can be thought of as a sort of countable completeness condition on the system of measures. is said to be -homogeneous if each is -complete. Homogeneous trees are involved in Martin and Steel's proof of projective determinacy. ==References==
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