Geodesic
Classifying Countable Boolean Terms
Algebra i logika, Tome 44 (2005) no. 2, pp. 173-197.

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We deal with the Borel and difference hierarchies in the space $P\omega$ of all subsets of $\omega$ endowed with the Scott topology. (The spaces $P\omega$ and $2^\omega$ coincide set-theoretically but differ topologically.) We look at the Wadge reducibility in $P\omega$. The results obtained are applied to the problem of characterizing $\omega_1$ – terms $t$ which satisfy $\mathcal C =t({\boldsymbol\Sigma}^0_1)$ for a given Borel – Wadge class $\mathcal C$. We give its solution for some levels of the Wadge hierarchy, in particular, all levels of the Hausdorff difference hierarchy. Finally, we come up with a discussion of some relevant facts and open questions.
Keywords: countable Boolean term, Wadge hierarchy, Hausdorff difference hierarchy, Borel hierarchy. 
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V. L. Selivanov. Classifying Countable Boolean Terms. Algebra i logika, Tome 44 (2005) no. 2, pp. 173-197. http://geodesic.mathdoc.fr/item/AL_2005_44_2_a2/

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