# Canonization of smooth equivalence relations on infinite-dimensional perfect cubes

@article{Kanovei2018CanonizationOS, title={Canonization of smooth equivalence relations on infinite-dimensional perfect cubes}, author={Vladimir Kanovei and Vassily A. Lyubetsky}, journal={arXiv: Logic}, year={2018} }

A canonization scheme for smooth equivalence relations on $\mathbb R^\omega$ modulo restriction to infinite perfect products is proposed. It shows that given a pair of Borel smooth equivalence relations $\mathsf E,\mathsf F$ on $\mathbb R^\omega$, there is an infinite perfect product $P\subseteq\mathbb R^\omega$ such that either ${\mathsf F}\subseteq{\mathsf E}$ on $P$, or, for some $j<\omega$, the following is true for all $x,y\in P$: $x\,\mathsf E \,y$ implies $x(j)=y(j)$, and $x\restriction… CONTINUE READING

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