The set of axioms of $ACF_p$ is infinite. Why is it decidable? Is there a way to decide given a number whether it is a code of some axiom of $ACF_p$
Asked
Active
Viewed 35 times
1
-
We have a finite list of axioms, plus the assertions that every monic polynomial of degree $\ge 1$ has a root. These axioms have a simple to describe shape. – André Nicolas Mar 01 '16 at 23:57
-
What is the context of your question? Any reasonable method of encoding syntax makes questions such as "is formula $\phi$ an axiom of $ACF_p$?" decidable (i.e., the test is effectively computable). However, it is possible to devise unreasonable encodings which make life much harder. – Rob Arthan Mar 02 '16 at 00:12