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Surjectively rigid chains
Author(s) -
MontalvoBallesteros Mayra,
Truss John K.
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000014
Subject(s) - uncountable set , mathematics , endomorphism , mathematical proof , rigidity (electromagnetism) , automorphism , axiom , pure mathematics , discrete mathematics , combinatorics , geometry , physics , countable set , quantum mechanics
We study rigidity properties of linearly ordered sets (chains) under automorphisms, embeddings, epimorphisms, and endomorphisms. We focus on two main cases: dense subchains of the real numbers, and uncountable dense chains of higher regular cardinalities. We also give a Fraenkel‐Mostowski model which illustrates the role of the axiom of choice in one of the key proofs.