John Truss

Surjectively rigid chains

A classical result of Dushnik and Miller establishes the existence of a dense subchain of the ordered set of real numbers, which has no automorphisms, apart from the identity. In joint work with Manfred Droste, we showed that such rigid chains can be constructed which nevertheless admit many non-trivial embeddings (order-isomorphisms to subsets), and constructions are also given of any uncountable regular cardinality which are rigid for automorphisms, but which admit many non-trivial embeddings; in this case, stationary sets are used to encode a dense set of p[pints in the order constructed. In joint work with Mayra Montalvo-Ballesteros, these results are extended to consider also epimorphisms (order-preserving surjections) and in some cases, general endomorphisms.