Pseudofiniteness and measurability of the everywhere infinite forest

2023/09/02 by DARÍO GARCÍA, García, Darío, MELISSA ROBLES +1
#03C (Primary) 05C (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2309.00991

Abstract

In this paper we study the theories of the infinite-branching tree and the r-regular tree, and show that both of them are pseudofinite. Moreover, we show that they can be realized by infinite ultraproducts of polynomial exact classes of graphs, and so they are also generalised measurable.

Related

• Infinite trees
• Pseudo-finiteness of arbitrary graphs of bounded shrub-depth
• The Uniform Measure of Simple Regular Sets of Infinite Trees
• The Expansion Problem for Infinite Trees
• A simple continuous theory