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  1. The arithmetic of cuts in models of arithmetic.Richard Kaye - 2013 - Mathematical Logic Quarterly 59 (4-5):332-351.
    We present a number of results on the structure of initial segments of models of Peano arithmetic with the arithmetic operations of addition, subtraction, multiplication, division, exponentiation and logarithm. Each of the binary operations introduced is defined in two dual ways, often with quite different results, and we attempt to systematise the issues and show how various calculations may be carried out. To understand the behaviour of addition and subtraction we introduce a notion of derivative on cuts, analogous to differentiation (...)
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