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    The Mostowski model is constructed within ZF set theory, ... — Carmelics
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    Challenges→In the Mostowski model, the set A of rationals can be linearly ordered but cannot be well-ordered.

    The Mostowski model is constructed within ZF set theory, which itself presupposes classical logic and standard set-theoretic semantics.

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    Reasons For

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    • 1.ZF axioms are explicitly formulated in first-order classical logic with bivalent truth values.
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    • 2.The Mostowski collapse lemma relies on classical proof techniques, particularly excluded middle.
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    • 3.Standard set-theoretic semantics assigns determinate membership relations, presupposing classical semantics.
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    Reasons Against

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    • 1.Constructive mathematics builds set theories in intuitionistic logic without classical presuppositions.
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    • 2.The Mostowski model can be formalized in weaker logical systems, showing logical presupposition is not inevitable.
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    • 3.Alternative semantics (fuzzy, many-valued) preserve Mostowski's structural results differently.
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    Related

    Alternative semantics (fuzzy, many-valued) preserve Mostowski's structural resul...Constructive mathematics builds set theories in intuitionistic logic without cla...In the Mostowski model, the set A of rationals can be linearly ordered but canno...Standard set-theoretic semantics assigns determinate membership relations, presu...
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    The Mostowski collapse lemma relies on classical proof techniques, particularly ...The Mostowski model can be formalized in weaker logical systems, showing logical...ZF axioms are explicitly formulated in first-order classical logic with bivalent...

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