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When does elementary bi-embeddability imply isomorphism? | | John Goodrick
; | | Date: |
13 May 2007 | | Subject: | Logic (math.LO) | | Abstract: | A first-order theory has the Schroder-Bernstein property if any two of its
models that are elementarily bi-embeddable are isomorphic. We prove that if a
countable theory T has the Schroder-Bernstein property then it is classifiable
(it is superstable and has NDOP and NOTOP) and satisfies a slightly stronger
condition than nonmultidimensionality, namely: there cannot be a model M of T,
a type p over M, and an automorphism f of M such that for every two distinct
natural numbers i and j, f^i(p) is orthogonal to f^j(p). We also make some
conjectures about how the class of theories with the Schroder-Bernstein
property can be characterized. | | Source: | arXiv, arxiv.0705.1849 | | Services: | Forum | Review | PDF | Favorites | |
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