Vaught’s conjecture on analytic sets

Hjorth, Greg¹

¹ Department of Mathematics, University of California, Los Angeles, California 90095-1555

Journal of the American Mathematical Society, Tome 14 (2001) no. 1, pp. 125-143

Résumé

Let $G$ be a Polish group. We characterize when there is a Polish space $X$ with a continuous $G$-action and an analytic set (that is, the Borel image of some Borel set in some Polish space) $A\subset X$ having uncountably many orbits but no perfect set of orbit inequivalent points. Such a Polish $G$-space $X$ and analytic $A$ exist exactly when there is a continuous, surjective homomorphism from a closed subgroup of $G$ onto the infinite symmetric group, $S_\infty$, consisting of all permutations of $\mathbb {N}$ equipped with the topology of pointwise convergence.

Détail

DOI : 10.1090/S0894-0347-00-00349-0

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