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Pré-Publication, Document De Travail Année : 2014

DICHOTOMY THEOREMS FOR FAMILIES OF NON-COFINAL ESSENTIAL COMPLEXITY

Résumé

We prove that for every Borel equivalence relation $E$, either $E$ is Borel reducible to $\mathbb{E}_0$, or the family of Borel equivalence relations incompatible with $E$ has cofinal essential complexity. It follows that if $F$ is a Borel equivalence relation and $\cal F$ is a family of Borel equivalence relations of non-cofinal essential complexity which together satisfy the dichotomy that for every Borel equivalence relation $E$, either $E\in {\cal F}$ or $F$ is Borel reducible to $E$, then $\cal F$ consists solely of smooth equivalence relations, thus the dichotomy is equivalent to a known theorem.
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Dates et versions

hal-01098837 , version 1 (29-12-2014)

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John D. Clemens, Dominique Lecomte, Benjamin D. Miller. DICHOTOMY THEOREMS FOR FAMILIES OF NON-COFINAL ESSENTIAL COMPLEXITY. 2014. ⟨hal-01098837⟩
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