STRUCTURES ELEMENTARILY CLOSED RELATIVE TO THE NATURAL NUMBERS.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1968
- Accession Number
- AD0683294
Entities
People
- Eugene W. Madison
Organizations
- University of Iowa