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Appalachian Set Theory Workshop on Coherent Sequences

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 C-sequence is a
sequence C : < 1 so that the following holds for any < 1,
1. C+1 = {}, and
2. if is a non-zero 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-
The porpouse of this section is to stablish some of the basic structures and
properties linked to a C-sequence. 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


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics