Accession Number : AD0683294

Title :   STRUCTURES ELEMENTARILY CLOSED RELATIVE TO THE NATURAL NUMBERS.

Descriptive Note : Technical rept.,

Corporate Author : IOWA UNIV IOWA CITY DEPT OF MATHEMATICS

Personal Author(s) : Madison,Eugene W.

Report Date : DEC 1968

Pagination or Media Count : 11

Abstract : 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)

Descriptors :   (*ALGEBRA, *NUMBER THEORY), COMPLEX NUMBERS, GROUPS(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE