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    If the ordinal assignment presupposes a semantic model of... — Carmelics
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    Challenges→A proof of a sequent in first-order arithmetic gives rise to a well-founded reduction tree

    If the ordinal assignment presupposes a semantic model of well-ordering, the 'well-founded' character of the reduction tree is inherited from that model, not derived from the proof structure itself.

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    Key Terms

    Inherited(in logic)
    In this context, it means a property or characteristic that comes from something else, rather than being created independently.
    Ordinal assignment(in logic and mathematics)
    A way of assigning numbers or rankings to things in a specific order, where the position matters (like first place, second place, third place).
    Proof structure(in logic and mathematics)
    The way an argument or logical demonstration is organized—the steps and reasoning used to show something is true.
    Reduction tree(in logic and proof theory)
    A diagram that shows how a complicated problem or statement breaks down into simpler parts, branching like an upside-down tree.
    Semantic model(in logic and philosophy of language)

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    A system that represents what words or symbols actually mean and how they relate to real things or abstract ideas.
    Well-founded(as used in epistemology)
    Supported by good reasons, solid evidence, or logical justification; not arbitrary or baseless.
    Well-ordering(in mathematics and logic)
    An arrangement where every item has a specific position and there's always a clear 'first' item—like how the numbers 1, 2, 3 are ordered, but a messy pile of objects wouldn't be.

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

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    A proof of a sequent in first-order arithmetic gives rise to a well-founded redu...

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