Journal of Symbolic Logic 62 (2):595-607 (1997)

We give positive answers to two open questions from [15]. (1) For every set C countably determined over A, if C is Π 0 α (Σ 0 α ) then it must be Π 0 α (Σ 0 α ) over A, and (2) every Borel subset of the product of two internal sets X and Y all of whose vertical sections are Π 0 α (Σ 0 α ) can be represented as an intersection (union) of Borel sets with vertical sections of lower Borel rank. We in fact show that (2) is a consequence of the analogous result in the case when X is a measurable space and Y a complete separable metric space (Polish space) which was proved by A. Louveau and that (1) is equivalent to the property shared by the inverse standard part map in Polish spaces of preserving almost all levels of the Borel hierarchy
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DOI 10.2307/2275548
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Foundations of Infinitesimal Stochastic Analysis.K. D. Stroyan - 1988 - Journal of Symbolic Logic 53 (4):1261-1262.
Graphs with ∏ 1 0 (K)Y-Sections.Boško Živaljević - 1993 - Archive for Mathematical Logic 32 (4):259-273.
Every Borel Function is Monotone Borel.Boško Živaljević - 1991 - Annals of Pure and Applied Logic 54 (1):87-99.

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