Vol. 29, No. 1, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Indefinability in the arithmetic isolic integers

Philip Olin

Vol. 29 (1969), No. 1, 175–186
Abstract

This paper is primarily concerned with the theory of the arithmetic isolic integers. The following results are obtained:

(1) No nonfinite member of the arithmetic isolic integers Λ(A) can be defined in Λ(A) even by an infinite number of arithmetic formulas (Theorem 4).

(2) The arithmetic isols Λ(A) cannot be defined in Λ(A) even by an infinite number of arithmetic formulas (Theorem 7).

(3) We exhibit some nonstandard models of arithmetic contained within Λ(A) (Theorem 10).

The first result above follows from recent work of Nerode in the theory of isols, while the second strengthens his results to obtain the desired conclusion.

Mathematical Subject Classification
Primary: 02.70
Milestones
Received: 13 May 1968
Published: 1 April 1969
Authors
Philip Olin