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    If κ's position in the inaccessible hierarchy is model-re... — Carmelics
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    Challenges→A weakly compact inaccessible cardinal cannot be the first, second, or any finitely indexed inaccessible cardinal

    If κ's position in the inaccessible hierarchy is model-relative, then 'κ cannot be the nth inaccessible' is not an absolute claim but a schema relativized to a background universe.

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    Key Terms

    Absolute claim(as used in epistemology and metaphysics)
    A statement that is true regardless of circumstances or context, in all situations—contrasted with claims that are only true under certain conditions.
    Background universe(as used in set theory and mathematical logic)
    The underlying mathematical world or set of assumptions you're working within—like the 'rules of the game' that frame what's possible.
    Schema(as used in logic)
    A basic pattern or framework that represents the structure of something—in this case, a logical argument stripped down to its simplest form.
    hierarchy(as used in logic and argumentation)
    A ranking system that puts some things in order from most to least important, valuable, or protected.
    inaccessible cardinal

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    (Large cardinal assumption in the structuralist account)
    A cardinal number large enough to serve as the cardinality of the mereological atoms in the universe, enabling the structuralist construction of set theory.
    model-relative(describing properties in logic and mathematics)
    Dependent on which particular version or interpretation of a system you're looking at; something can be true in one model but not in another.
    κ (kappa)(mathematical notation)
    A symbol used in set theory to represent a large cardinal number (roughly: a really, really big number with special properties).

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    Modality & Possibility1 linked

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    A weakly compact inaccessible cardinal cannot be the first, second, or any finit...

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