Proving finitely many orbit types for definable sets in an o-minimal structure, suggesting new insights into definable theories.
Let N = (R, +, •, <, . . . ) be an o-minimal expansion of the standard structure of a real closed field R. Let G be a definable group and X a definable proper definable G set.We prove that X has only finitely many orbit types.We also prove equivariant definable Tietze extension theorem.
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Tomohiro KAWAKAMI (2016) studied this question.
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