… We discuss the connection between decidability of a theory of a large algebraic extensions
of Q and the recursiveness of the field as a subset of a fixed algebraic closure. In particular, we …

… ‘close to Q’ tend to be decidable. Therefore, it is a challenge to find decidable algebraic fields
… A different line of research on decidable theories of algebraic fields started much earlier. …

… 1, we prove the algebraic results necessary for ? 2. It is first shown … decidable fields C1, C2,
... from a given decidable field C0. Furthermore, if C is any one of the known decidable fields …

… class of algebraically closed fields, then Th(ALC) is decidable. … , by employing the classical
algebraic elimination theory. … Next we consider the theory ALC of algebraically closed fields. …

… In particular, we will show that the V3 theory of algebraic number fields is decidable (Theorem
3.3). Hence the V3 theory of finitely generated subfields of the complex number …

… of fields … , decidable field K c Q, where Q is the algebraic closure of Q, the rational numbers.
This is a direct construction; in fact, the field K is recursive, ie K is a recursive set and the field …

… We say a mathematical theory is decidable if there is an effective … each statement of an
undecidable theory into an equivalent … problem for fields of finite degree over the rationals. 1 …

… in the theory of algebraically closed valued fields (ACVF) … themselves decidable, then the
valued field as a whole is decidable; … a decision procedure for the valued field. Let us point out …

… decidable, while for normed spaces, only the most trivial example, namely the theory of a
1-dimensional space, is decidable. … and the symbols for the field operations and the ordering to …

… the field Q of rational numbers regarded as a linearly ordered field such that for n E w, all
elements of the field … In conclusion, we give an example of a complete decidable theory only the …