Transfinite large inductive dimensions modulo absolute Borel classes

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Abstract

The following inequalities between transfinite large inductive dimensions modulo absolutely additive (resp. multiplicative) Borel classes <I>A</I>(α) (resp. <I>M</I>(α)) hold in separable metrizable spaces:<BR> (i) <I>A</I>(0)-trInd≥<I>M</I>(0)-trInd≥max{<I>A</I>(1)-trInd, <I>M</I>(1)-trInd}, and<BR> (ii) min{<I>A</I>(α)-trInd, <I>M</I>(α)-trInd}≥max{<I>A</I>(β)-trInd, <I>M</I>(β)-trInd}, where 1≤α<β<ω<SUB>1</SUB>.<BR> We show that for any two functions <I>a</I> and <I>m</I> from the set of ordinals Ω={α:α<ω<SUB>1</SUB>} to the set {−1}∪Ω∪{∞} such that<BR> (i) <I>a</I>(0)≥<I>m</I>(0)≥max{<I>a</I>(1), <I>m</I>(1)}, and<BR> (ii) min{<I>a</I>(α),<I>m</I>(α)}≥max{<I>a</I>(β),<I>m</I>(β)}, whenever 1≤α<β<ω<SUB>1</SUB>,<BR> there is a separable metrizable space <I>X</I> such that <I>A</I>(α)-trInd<I>X</I>=<I>a</I>(α) and <I>M</I>(α)-trInd<I>X</I>=<I>m</I>(α) for each 0≤α<ω<SUB>1</SUB>.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 61(2), 327-344, 2009-04-01

    The Mathematical Society of Japan

References:  12

Codes

  • NII Article ID (NAID)
    10024905666
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    10207715
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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