Universal flows and automorphisms of \mathcal P(ω)/fin

2018/02/06 by Brian, Will
#Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1802.02055

Abstract

We prove that for every countable discrete group G, there is a G-flow on ω^* that has every G-flow of weight ≤ ℵ₁ as a quotient. It follows that, under the Continuum Hypothesis, there is a universal G-flow of weight ≤ \mathfrakc. Applying Stone duality, we deduce that, under CH, there is a trivial automorphism τ of \mathcal P(ω)/fin with every other automorphism embedded in it, which means that every other automorphism of \mathcal P(ω)/fin can be written as the restriction of τ to a suitably chosen subalgebra.

Related

• Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
• Veech's Theorem of G acting freely on G^\textrmLUC and Structure Theorem of a.a. flows
• Automorphisms of \mathcal P(ω)/fin and large continuum
• Topological dynamics of automorphism group of countably categorical\n structures
• The homeomorphism group of the universal Knaster continuum