
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 elementarilyclosed 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