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Some results about borel sets in descriptive set theory of hyperfinite sets

Boško Živaljević

Journal of Symbolic Logic 55 (2):604-614 (1990)

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Every Borel function is monotone Borel.Boško Živaljević - 1991 - Annals of Pure and Applied Logic 54 (1):87-99.details Given two internal sets X and Y we prove that every Borel function whose graph is a subset of the product X x Y is a member of the least set containing the class of all internal functions and closed with respect to the operations of monotone countable union and intersection. We also prove that any Souslin function can be extended to a Borel function and obtain, as a corollary, a new proof of the recent result of Henson and Ross (...) Download Export citation Bookmark 1 citation
Graphs with ∏ 1 0 (K)Y-sections.Boško Živaljević - 1993 - Archive for Mathematical Logic 32 (4):259-273.details We prove that a Borel subset of the product of two internal setsX andY all of whoseY-sections are ∏ 1 0 (K)(∑ 1 0 (K)) sets is the intersection (union) of a countable sequence of Borel graphs with internalY-sections. As a consequence we prove some standard results about the domains of graphs in the product of two topological spaces all of whose horizontal section are compact (open) sets. A version of classical Vitali-Lusin theorem for those types of graphs is given (...) Download Export citation Bookmark 1 citation

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