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

Tags

DTIC Thesaurus Topics

  • Automata
  • Complex Numbers
  • Numbers
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.