Can integers be defined in the first-order theory of the rationals?

406 Views Asked by At

Can integers be defined in the first-order theory of the rationals with addition, multiplication, and order?

1

There are 1 best solutions below

0
On BEST ANSWER

Yes. It's a much celebrated theorem of Julia Robinson.

Julia Robinson, Definability and Decision Problems in Arithmetic. The Journal of Symbolic Logic, Vol. 14, No. 2 (Jun., 1949) , pp. 98-114