Timeline for Does every set admit a rigid binary relation? (and how is this related to the Axiom of Choice?)
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| Nov 21, 2009 at 1:38 | comment | added | Mike Shulman | As saf said below, this paper does use AC. It is, of course, completely trivial that under AC, every set admits a relation (namely, a well-ordering) which is rigid in the sense of this question (and of my original one), namely, admitting no nontrivial AUTOmorphisms. What Vopenka-Pultr-Hedrlin prove is that in fact (assuming AC) there is a relation on any set which admits no nontrivial ENDOmorphisms. No infinite well-ordering has this property. | |
| Nov 20, 2009 at 21:28 | comment | added | Joel David Hamkins | Thanks! I admire Vopenka very much, so I'm pleased he answered this. I'll get back to you once I look this up... | |
| Nov 20, 2009 at 18:56 | history | answered | Kristal Cantwell | CC BY-SA 2.5 |