The automorphism group of the random poset does not admit a generic pair

2020/12/08 by Kwiatkowska, Aleksandra, Panagiotopoulos, Aristotelis
#06A99 #20B27 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2012.04376

Abstract

We show that the conjugacy class of every pair of automoprhisms of the random poset is meager. This answers a question of Truss; see also Kuske-Truss. EDIT. Work in progress, at the moment there is a gap in the proof of Theorem 2.

Related

• The structure of generic automorphisms of the random poset
• The structure of random automorphisms of the random graph
• The structure of random automorphisms of countable structures
• Non-genericity phenomenon in some ordered Fraisse classes
• Automorphism groups of randomized structures