Vol. 37, No. 2, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Relations not determining the structure of L

John William Rosenthal

Vol. 37 (1971), No. 2, 497–514
Abstract

A relation S is said to be determined up to isomorphism by relations R with respect to a theory K if for all models A1,A2 of K,A1 restricted to R is isomorphic to A2 restricted to R implies A1 is isomorphic to A2. In this paper simple necessary conditions for S to be determined up to isomorphism by R are given. These are applied in set theory to show there are (nonstandard) models of set theory with isomorphic ordinals and nonisomorphic constructible sets. The isomorphism on the ordinals may be taken to preserve many familiar arithmetic functions on the ordinals as addition, multiplication and exponentiation.

Mathematical Subject Classification
Primary: 02H15
Secondary: 02K99
Milestones
Received: 31 July 1969
Revised: 10 February 1970
Published: 1 May 1971
Authors
John William Rosenthal