Numbers

Here is the current draft (April 27, 2011) of a paper about the logical development of the so-called natural numbers. The paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. See also another paper, Induction and Recursion. Meanwhile, here is “Numbers” (31 pp., size A4):

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This paper is also posted at arXiv.org.

The von Neumann construction of the ordinal numbers includes a construction of natural numbers as a special kind of ordinal. In any case, the natural numbers can be understood as composing a free algebra in a certain signature, {0,s}. The paper here culminates in a construction of, for each algebraic signature S, a class ON_S that is to the class of ordinals as S is to {0,s}. In particular, ON_S has a subclass that is a free algebra in the signature S.

For the sake of editing the paper further, I wrote several pages about the version of January 12, 2010, identifying its main points:

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Here, for the record, is that January 12 edition:

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