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arXiv · 2505.00633

Strong Rigidity and Elementary Embeddings

Marwan Salam Mohammd
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Abstract

We present a method for producing elementary embeddings from homomorphisms. This method is utilized in the study of the "strongly rigid relation principle" as defined by Hamkins and Palumbo in their paper "The Rigid Relation Principle, a New Weak Choice Principle." We establish that the strongly rigid relation principle is also a weak choice principle that is independent of ZF. Finally, we characterize proto Berkeley cardinals in terms of a strong failure of the strongly rigid relation principle.

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Marwan Salam Mohammd. 2025-05-01. Strong Rigidity and Elementary Embeddings. https://arxiv.org/abs/2505.00633

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