Non-standard numbers: a semantic obstacle for modelling arithmetical reasoning
A. De Araujo, Walter Alexandre Carnielli · Logic Journal of IGPL · 2010
The existence of non-standard numbers in first-order arithmetics is a semantic obstacle for modelling our arithmetical skills. This article argues that so far there is no adequate approach to overcome such a semantic obstacle, because we can also find out, and deal with, non-standard elements in Turing machines.