Atlas: Partitions of sets of finite sequences of positive integers by Carlod Di Prisco

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Boise Extravaganza in Set Theory
March 23-25, 2001
Boise State University
Boise, ID, USA

Organizers
Tomek Bartoszynski, Paul Corazza, Justin Moore

Partitions of sets of finite sequences of positive integers
by
Carlod Di Prisco
IVIC
Coauthors: Jimena Llopis, Stevo Todorcevic

Partitions of sets of finite sequences of positive integers

Carlos A. Di Prisco

Work in collaboration with Jimena Llopis and Stevo Todorcevic will be presented. The main result deals with partitions of collections of finite products of finite sets of positive integers, and is is stated as follows.

There is a function h: \omega^{< \omega} --> \omega such that for every sequence {m_i}_{i < \omega} of positive integers and every partition

c:
È
j < \omega

Õ
i <= j
h(m₀, ... , m_i) --> 2,

there is a sequence [H\vec]={H_i}_{i < \omega} with H_i subset or equal h(m₀, ... , m_i) and |H_i|=m_i such that {j in \omega: c is constant on \prod_{i < j}H_i} is infinite.

Date received: March 21, 2001