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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

  8. add missing closing ’)’

    Luc Voo

    diff, v17, current

1 to 8 of 8

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