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    Carmelics

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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that XL satisfies Compactness and Löwenheim-Skolem

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The translation from XL to MSL via Delta may not preserve all semantic content if sort-relativized quantifiers lack exact MSL correlates.
      ?

      Think about whether this reason is strong or weak

    • 2.Löwenheim-Skolem for MSL depends on Skolem functions ranging over unsorted domains, but XL's sort constraints may block required witness construction.
      ?

      Think about whether this reason is strong or weak

    • 3.If Delta itself is an infinite theory, compactness transfer requires Delta's own compactness, creating a circularity in the proof strategy.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Barwise and Feferman's work on generalized logics shows that adding expressive mechanisms to first-order logic routinely sacrifices Löwenheim-Skolem.
      ?

      Think about whether this reason is strong or weak

    • 2.XL's sort-indexed expressions constitute a genuine increase in expressive power over unsorted FOL, making metalogical property inheritance non-trivial.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The Main Theorem establishes that consequence in XL is equivalent to consequence of translations in MSL modulo theory Delta
      ?

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    • 2.XL satisfies Compactness and Löwenheim-Skolem
      ?

      Think about whether this reason is strong or weak

    • 3.The Main Theorem transfers these properties from MSL to XL
      ?

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