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    Woodin's work on the inner model program suggests that su... — Carmelics
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    Challenges→Small large cardinal axioms are compatible with V=L, unlike measurable cardinals

    Woodin's work on the inner model program suggests that sufficiently strong small large cardinals may eventually yield incompatibility with V=L, undermining the stability of the claimed dichotomy.

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    Key Terms

    Inner model program(as used in set theory)
    A research project in logic aimed at understanding and constructing different mathematical universes that sit inside larger mathematical frameworks.
    V=L(Set theory; Gödel's constructible universe)
    The statement asserting that all sets are constructible
    Woodin(as the subject of the statement about mathematical foundations)
    W. Hugh Woodin is a mathematician who studies set theory, the branch of math that deals with collections of objects and their properties. He's known for making major discoveries about the deepest levels of mathematical reality.
    dichotomy(Refers to one of Zeno's paradoxes of motion)
    A paradox so named because it involves repeated division into two
    incompatibility

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    (Characterized as an apparently negative notion, which creates a problem for the positive truth-maker proposal.)
    A relation that obtains between two states when it is not possible for them to obtain together.
    large cardinals(Contemporary set theory proposes large cardinal axioms as a remedy for the incompleteness of ZFC.)
    Set-theoretic principles positing the existence of very large infinite cardinal numbers, used as candidate new axioms to extend ZFC and potentially settle open questions such as the Continuum Hypothesis.

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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    Small large cardinal axioms are compatible with V=L, unlike measurable cardinals

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