The Schröder-Bernstein property for weakly minimal theories

2009/12/07 by John Goodrick, Goodrick, John, M. Laskowski +1 · 1 citation
Computer Science · Mathematics · #03C45 (Primary) #03C52 (Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.0912.1363

openalex publication_date 2009/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a countable, weakly minimal theory, we show that the Schroeder-Bernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to both a condition on orbits of rank 1 types and the property that the theory has no infinite collection of pairwise bi-embeddable, pairwise nonisomorphic models. We conclude that for countable weakly minimal theories, the Schroeder-Bernstein property is absolute between transitive models of ZFC.

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