 
Summary: Appalachian Set Theory
Workshop on Coherent Sequences
Lectures by Stevo Todorcevic
Notes taken by Roberto Pichardo Mendoza
1 Introduction
2 Preliminaries
Let's begin by defining the basic structure for our work. A Csequence is a
sequence C : < 1 so that the following holds for any < 1,
1. C+1 = {}, and
2. if is a nonzero limit ordinal, then
(a) sup C =
(b) o.t.(C) = , where o.t. stands for order type, and
(c) C does not contain any succesor ordinal.
For the rest of the notes C will always denote the th term of our C
sequence.
The porpouse of this section is to stablish some of the basic structures and
properties linked to a Csequence. We start with the upper and full lower trace.
2.1 Definition. Let < < 1.
1. The upper trace of the walk from to is defined as Tr(, ) = i : i
n , where
