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nLab > Latest Changes: Peano arithmetic

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    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 28th 2014

    I added some material to Peano arithmetic and Robinson arithmetic. At the latter, I replaced the word “fragment” (which sounds off to my ears – actually Wikipedia talks about thisterm a little) with “weakening”.

    Still some links to be inserted.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeNov 28th 2014

    I wrote a little bit about second-order being Peano’s original definition, and the categoricity (in the logician’s sense) of that system.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2014

    Thanks! I have added hyperlinks.

    The third clause of the first-order axioms needs parenthesis, I would say! What do you think?

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 28th 2014

    Urs, please go ahead and add parentheses if you feel it would help; thanks!

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2014

    Okay, did so.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 21st 2023

    added pointer to:

    diff, v13, current

  7. If there exists an elementary embedding j:M\to N, then M and N are elementarily equivalent. If all models of a theory are elementarily equivalent, then the theory is complete by the completeness theorem. This contradicts the incompleteness theorem.

    Robert Smith

    diff, v16, current

1 to 7 of 7

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