Quantifier alternation in a class of recursively defined tree properties

Moumanti Podder

Published 2019-02-14Version 1

Alternating quantifier depth is a natural measure of difficulty required to express first order logical sentences. We define a sequence of first order properties on rooted, locally finite trees in a recursive manner, and provide rigorous arguments for finding the alternating quantifier depth of each property in the sequence, using Ehrenfeucht-Fra\"{i}ss\'{e} games.