7 found
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  1.  19
    Some Results About Borel Sets in Descriptive Set Theory of Hyperfinite Sets.Boško Živaljević - 1990 - Journal of Symbolic Logic 55 (2):604-614.
  2.  8
    The Structure of Graphs All of Whose y-Sections Are Internal Sets.Boško Živaljević - 1991 - Journal of Symbolic Logic 56 (1):50-66.
  3.  36
    Lusin-Sierpinski Index for the Internal Sets.Boško Živaljević - 1992 - Journal of Symbolic Logic 57 (1):172 - 178.
    We prove that there exists a function f which reduces a given Π1 1 subset P of an internal set X of an ω1-saturated nonstandard universe to the set WF of well-founded trees possessing properties similar to those possessed by the standard part map. We use f to define the Lusin-Sierpinski index of points in X, and prove the basic properties of that index using the classical properties of the Lusin-Sierpinski index. An example of a Π1 1 but not Σ1 (...)
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  4.  9
    Graphs with ∏ 1 0 (K)Y-Sections.Boško Živaljević - 1993 - Archive for Mathematical Logic 32 (4):259-273.
    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 (...)
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  5.  5
    Every Borel Function is Monotone Borel.Boško Živaljević - 1991 - Annals of Pure and Applied Logic 54 (1):87-99.
    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 (...)
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  6.  32
    Louveau's Theorem for the Descriptive Set Theory of Internal Sets.Kenneth Schilling & Boško Živaljević - 1997 - Journal of Symbolic Logic 62 (2):595-607.
    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 (...)
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  7.  17
    U-Meager Sets When the Cofinality and the Coinitiality of U Are Uncountable.Bosko Zivaljevic - 1991 - Journal of Symbolic Logic 56 (3):906-914.
    We prove that every countably determined set C is U-meager if and only if every internal subset A of C is U-meager, provided that the cofinality and coinitiality of the cut U are both uncountable. As a consequence we prove that for such cuts a countably determined set C which intersects every U-monad in at most countably many points is U-meager. That complements a similar result in [KL]. We also give some partial solutions to some open problems from [KL]. We (...)
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