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- New Foundations for Geometry: Two Non-Additive Languages for Arithmetical Geometry
New Foundations for Geometry: Two Non-Additive Languages for Arithmetical Geometry
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Presents two simple generalizations of commutative rings. They form (co)-complete categories, that contain commutative (semi-) rings. But they also contains the "integers" (and ), and the "residue fields" (and ), of the real (and complex) numbers. Here is the collection of unit balls, and is the collection of spheres augmented with a. The initial object is "the field with one element".
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Patterson, William Davis / Maine Genealogical Society (1884- ). / Maine Probate Court (Lincoln Co ).