The uncountable cofinality of the automorphism group of the countable universal distributive lattice
نویسندگان
چکیده
We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.
منابع مشابه
The Automorphism Group of the Universal Distributive Lattice
We describe the normal subgroup lattice of the automorphism groups of the countable universal homogeneous distributive lattice and of the countable atomless generalized Boolean lattice. Also, we show that subgroups of these automorphism groups of index less than 2@0 lie between the pointwise and the setwise stabilizer of a nite set.
متن کاملUncountable cofinalities of automorphism groups of linear and partial orders
We demonstrate the uncountable cofinality of the automorphism groups of various linear and partial orders. We also relate this to the ‘Bergman’ property, and discuss cases where this may fail even though the cofinality
متن کاملUniversal sequences for the order-automorphisms of the rationals
In this paper, we consider the group Aut(Q, ≤) of order-automorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q, ≤) is contained in an N-generated subgroup of Aut(Q, ≤) for some fixed N ∈ N. We show that the least such N is 2. Moreover, for every countable subset of...
متن کاملCountable Structure Does Not Have a Free Uncountable Automorphism Group
It is proved that the automorphism-group of a countable structure cannot be a free uncountable groupi. The idea is that instead proving that every countable set of equations of a certain form has a solution, we prove that this holds for a co-meagre family of appropriate countable sets of equations. Can a countable structure have an automorphism group, which a free uncountable group? This was a ...
متن کاملTurbulence, Amalgamation, and Generic Automorphisms of Homogeneous Structures
We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...
متن کامل