11
$\begingroup$

I'm wondering if there is existing terminology to describe fields $F$ with the properties below. I don't have a completely precise description of the concept I have in mind, but hopefully this will be enough.

  1. Every element of $F$ requires only a finite amount of information to describe (so that it can be stored in a computer in some way).
  2. There exist (finite) algorithms which can be used implement the field operations of $F$.

For example, the field $\mathbb Q$ (and any finite extension of it) has these properties, but the fields $\mathbb R$ and $\mathbb Q_p$ (where $p$ is prime) do not. I would appreciate any help in formulating my question more precisely, and any references which might discuss this concept.

$\endgroup$
  • $\begingroup$ I think the title is a bit misleading. I thought you were after mathematics formalized using the computer. $\endgroup$ – Pedro Sánchez Terraf Mar 20 '18 at 10:53
16
$\begingroup$

You are looking at a computable field (if your focus is on the field), or a computable presentation of a field (if your focus is on the details of how elements and operations are coded). These objects are studied in computable structure theory.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.