The Intended Model of Arithmetic. An Argument from Tennenbaum's Theorem
Paula Quinon, Konrad Zdanowski · 2006
We present an argument that allows to determine the intended model of arithmetic using some cognitive assumptions and the assumptions on the structure of natural numbers. Those assumptions are as follows: the psychological version of the Church thesis, computability of addition and multiplication and first order induction. We justify the thesis that the notion of natural number is determined by any recursive ω-model of PA up to recursive isomorphism.