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