Automorphism groups of finite topological rank [article]

Itay Kaplan, Pierre Simon
2019 arXiv   pre-print
We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group of an ω-categorical structure can go down to reducts. Together, those results prove that a large number of ω-categorical structures that appear in the literature have an automorphism group of finite topological rank. In fact, we are not aware of any
more » ... al structure to which they do not apply (assuming the automorphism group has no compact quotients). We end with a few questions and conjectures.
arXiv:1709.01918v5 fatcat:hduwxtxlbndo7pvsfc3xw3w5he