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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.
I wrote a little bit about second-order being Peano’s original definition, and the categoricity (in the logician’s sense) of that system.
Thanks! I have added hyperlinks.
The third clause of the first-order axioms needs parenthesis, I would say! What do you think?
Urs, please go ahead and add parentheses if you feel it would help; thanks!
Okay, did so.
added pointer to:
Richard Dedekind, Was sind und was sollen die Zahlen? (1888) [scan: pdf, doi:10.1007/978-3-663-02788-1]
Richard Dedekind (transl. by W. Beman), The nature and meaning of numbers, Chapter II in: Essays on the Theory of Numbers, Chicago (1901) [Project Gutenberg, pdf]
Giuseppe Peano, Arithmetices principia, nova methodo exposita, [Wikipedia]
David E. Joyce, The Dedekind/Peano Axioms (2005) [pdf]
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