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    Home/Original/inverse
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    Inverse View

    It is not the case that Forcing constructions, as developed by Cohen, produce extensions of ground models where new syntactic proofs become available that were unavailable in the original model.

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    Reasons For

    1 perspective
    Reason for
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    • 1.New syntactic proofs in extensions merely reformulate existing logical relationships; they don't generate fundamentally new mathematical truths.
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    • 2.Availability of new proofs in richer models conflates semantic expressiveness with genuine proof creation; syntax remains formally equivalent.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Cohen's forcing adds new sets to models, expanding the proof-theoretic resources available for deriving statements about those sets.
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    • 2.Proofs in extensions can reference elements absent from ground models, enabling derivations impossible under original constraints.
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    • 3.Forcing demonstrates that set-theoretic independence results depend on model structure, confirming that syntactic derivability is model-relative.
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