# Gal Amram: The better quasi order

Shalom,
we have seminar in Logic and Topology this week, June, 1.
Time : 14:00-16:00, Seminar room 201.
Speaker: Gal Amram(BGU)
Title: The better quasi order

Abstract:
A well quasi order (wqo) is a well founded quasi order (qo) with no infinite antichain.
In 1965 Nash-Williams introduced the notion of better quasi order (bqo) which generalized the wqo property.
Nash-Williams used the bqo notion to prove that the class of infinite graphs with no cycles are
bqo (and hence wqo) under a certain e! mbedding relation. The goal of the talk is to introduced the bqo
property and explain why better quasi order is better. I will prove the following theorem: Q bqo iff for every ordinal alpha, the
alpha power set of Q, P^{alpha}(Q) is wqo iff the omega_1 power set of Q, P^{alpha_1}(Q), is wqo.