Abstract: We consider fields computable in polynomial time (P-computable). We prove that under some assumptions about a P-computable field $ (A, +, \cdot) $ of characteristic $0$, there exists a P-computable field $ (B, +, \cdot) \cong (A, +, \cdot) $, in which $x^{-1}$ is not a primitive recursive function. In particular, this holds for the field $ \mathbb Q $ of rational numbers.

Cite: Alaev P.
P-computable structures in some algebraic classes
Twenty Years of Theoretical and Practical Synergies : 20th Conference on Computability in Europe 08-12 Jul 2024