This reminds me of Problem 1 in Donald J Newman's "Problem Seminar": Derive the operations of addition, subtraction, multiplication, and division from subtraction and reciprocal. On Fri, Jul 20, 2012 at 5:09 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Pressburger arithmetic deals with the theory of addition, more or less, and is decidable.
My recent fiddling with gcd reminded me that adding "inversion" (1/x) to addition is strictly less powerful than adding multiplication. Notice that simply adding inversion doesn't give you division (y/x), because that would require multiplication (y*(1/x)).
Has anyone studied Pressburger plus inversion? Just off-hand, I would guess that it is still decidable, and perhaps not increase the complexity all that much.
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