Homogeneous families and their automorphism groups

Mathematics – Logic

Scientific paper

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Scientific paper

A homogeneous family of subsets over a given set is one with a very ``rich''
automorphism group. We prove the existence of a bi-universal element in the
class of homogeneous families over a given infinite set and give an explicit
construction of $2^\cont$ isomorphism types of homogeneous families over a
countable set.

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