MSO 0-1 law for recursive random trees

TL;DR

This paper establishes the monadic second order 0-1 law for specific recursive tree models, highlighting differences in logical properties between tree and non-tree models.

Contribution

It proves the monadic second order 0-1 law for uniform and preferential attachment trees and shows the first order 0-1 law fails for non-tree models.

Findings

MSO 0-1 law holds for uniform attachment trees

MSO 0-1 law holds for preferential attachment trees

First order 0-1 law does not hold for non-tree models

Abstract

We prove the monadic second order 0-1 law for two recursive tree models: uniform attachment tree and preferential attachment tree. We also show that the first order 0-1 law does not hold for non-tree uniform attachment models.