Homogeneous families and their automorphism groups

1994/09/06 by Menachem Kojman, Saharon Shelah, Kojman, Menachem +1
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/9409205

published as J. London Math. Soc. (2) 52 No. 2 (1995) 303--317

arxiv created 1994/09/06 · arxiv updated 2009/11/30

Abstract

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.

Related

• Set-homogeneous hypergraphs
• Automorphism groups of universal diversities
• Infinite homogeneous bipartite graphs with unequal sides
• Uniform homogeneity
• Class-Preserving Automorphisms of a Family of Finite p-Groups