-equivalence, isomorphism and potential isomorphism

Authors:
Mark Nadel and Jonathan Stavi

Journal:
Trans. Amer. Math. Soc. **236** (1978), 51-74

MSC:
Primary 02H10; Secondary 02K05, 02H13

DOI:
https://doi.org/10.1090/S0002-9947-1978-0462942-3

MathSciNet review:
0462942

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Abstract: It is well known that two structures are -equivalent iff they are potentially isomorphic [that is, isomorphic in some (Cohen) extension of the universe]. We prove that no characterization of -equivalence along these lines is possible (at least for successor cardinals ) and the potential-isomorphism relation that naturally comes to mind in connection with is often not even transitive and never characterizes for . A major part of the work is the construction of -like linear orderings (also Boolean algebras) A, B such that , where means: A and B are nonisomorphic -equivalent structures of cardinality .

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0462942-3

Article copyright:
© Copyright 1978
American Mathematical Society