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    It is not the case that If 'Zermelo's axioms' denotes Z rather than ZF, some independence results require separate proofs, since Z and ZF have different proof-theoretic strengths.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Most classical independence results (CH, AC independence) hold in both Z and ZF since they operate within comparable constructible hierarchies.
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    • 2.The historical convention names 'Zermelo's axioms' as ZF (including Replacement), making the claim's conditional premise ambiguous or non-standard.
      ?

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    • 3.Practical mathematics rarely depends on Z-specific limitations; independence proofs that differ between systems are specialized technical concerns, not central theorems.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Z lacks the Axiom of Replacement, which is essential for constructing hierarchies beyond V_ω, affecting transfinite induction proofs.
      ?

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    • 2.Independence results like CH require different proof strategies in Z versus ZF due to differing proof-theoretic ordinals (ω_1^CK vs higher).
      ?

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    • 3.Confusing Z and ZF in mathematical literature creates pedagogical problems, since results proven in ZF may be unprovable or require modification in Z.
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