STRUCTURES ELEMENTARILY CLOSED RELATIVE TO THE NATURAL NUMBERS.
IOWA UNIV IOWA CITY DEPT OF MATHEMATICS
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The paper discusses certain model theoretic properties of computable structures or arithmetically definable structures. In particular, it is shown that every arithmetically definable ordered subfield of real numbers is elementarily-closed relative to the natural numbers. Among the examples of fields which are not elementarily closed, we give an example of a subfield of complex numbers. It is shown that not every arithmetically definable field is elementarily closed. Author
- Theoretical Mathematics