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    The consistency of ZFC+φ+V=L establishes only proof-theor... — Carmelics
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    Challenges→Small large cardinal axioms are compatible with V=L, unlike measurable cardinals

    The consistency of ZFC+φ+V=L establishes only proof-theoretic compatibility, not genuine ontological cohabitation in any intended model.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Consistency proofs only show absence of derivable contradiction, not that any model actually satisfies all axioms simultaneously.
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    • 2.V=L is a contentious principle rejected by many set theorists; proof-theoretic compatibility doesn't resolve foundational disagreements.
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    • 3.Intended models require semantic satisfaction conditions beyond formal derivability; consistency is insufficient for ontological claims.
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    Reasons Against

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    Reason against
    ?
    • 1.If ZFC+φ+V=L is consistent, then by completeness theorem, some model exists satisfying all three components genuinely, not just formally.
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    • 2.Proof-theoretic compatibility *is* the standard criterion for ontological cohabitation in modern model theory and mathematical logic.
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    • 3.Distinguishing 'proof-theoretic' from 'genuine' ontological cohabitation assumes an unexplained metaphysical standard beyond mathematical semantics.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Consistency proofs only show absence of derivable contradiction, not that any mo...Distinguishing 'proof-theoretic' from 'genuine' ontological cohabitation assumes...If ZFC+φ+V=L is consistent, then by completeness theorem, some model exists sati...Intended models require semantic satisfaction conditions beyond formal derivabil...
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    Proof-theoretic compatibility *is* the standard criterion for ontological cohabi...Small large cardinal axioms are compatible with V=L, unlike measurable cardinalsV=L is a contentious principle rejected by many set theorists; proof-theoretic c...

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    claim
    Perspectives
    2 (1 for, 1 against)
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