Department of Mathematical Informatics | Graduate School of Informatics | Nagoya University

Big Questions

  1. Decomposability conjecture:
    Can we generalize the Jayne-Rogers theorem to higher Borel ranks?
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  2. Second-level Borel isomorphism types of strongly infinite dimensional compacta:
    Does every strongly infinite dimensional compactum second-level Borel isomorphic to the Hilbert cube?
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  3. First-level Borel isomorphism types of arc-like continua:
    How many first-level Borel isomorphism types of arc-like continua do there exist?
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  4. The existence of a non-σ-punctiform space:
    Is the Hilbert cube non-σ-punctiform?
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  5. σ-embedding of the Hilbert cube into a T1 space:
    Can the Hilbert cube be σ-embedded into the product of countably many copies of ω, each of which is endowed with the cofinite topology?
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Small Questions

  1. A half-Cohen real in computability theory:
    Develop a forcing with infinite dimensional compact subsets of a Henderson compactum in computability theory.
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  2. Constructing a Cantor manifold in a Scott ideal:
    Let x be a PA degree. Does every n-dimensional co-c.e. closed subset of the Hilbert cube have an n-dimensional Cantor manifold which is co-c.e. relative to x?
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  3. Iterates of choosing points from convex sets:
    Is the third iterate of the convex choice principle Weihrauch reducible to some finite parallel use of the second iterate?
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  4. Computability of points in locally contractible continua:
    Does every contractible, locally contractible, co-c.e., planar, continuum contain a computable point?
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