Re: Has BS Anand Refuted Gödel's Theorem

On Jan 8, 8:28 am, LauLuna <laureanol...@xxxxxxxx> wrote:

If we drop Completeness, then PA can be categorical, like second order
PA, and still incomplete, again like second order PA.

But I wonder what could it mean to "drop completeness" for first order
logic?



.

Relevant Pages

  • Re: Godels Incompleteness and Nonmonotonic Logic
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  • Re: Godels Incompleteness and Nonmonotonic Logic
    ... order theories which contain a modicum of elementary arithmetic can be ... shown to be either inconsistent or incomplete, ... Second order logic is incomplete in the sense that there is no complete ... containing a fragment elementary arithemtic and deductive system ...
    (sci.logic)
  • Re: Godels Incompleteness and Nonmonotonic Logic
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  • Re: Godels Incompleteness and Nonmonotonic Logic
    ... then A is provable from T. Obviously first order logic is not ... > shown to be either inconsistent or incomplete, ... there is indeed a deep link between completeness ... provability in L becomes a predicate of the first order ...
    (sci.logic)
  • Re: Cardinality and injection
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