Vol. 37, No. 2, 1971

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Relations not determining the structure of L

John William Rosenthal

Vol. 37 (1971), No. 2, 497–514

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
Received: 31 July 1969
Revised: 10 February 1970
Published: 1 May 1971
John William Rosenthal