Canonizing partition theorems: Diversification, products, and iterated versions
The author presents an abstract framework for canonizing partition theorems. From the introduction: ''This paper is concerned with canonizing partition theorems. The interest in such results originated with the Erdős-Rado theorem. But certainly the pigeonhole principle, asserting that for every mapping \(f: N\to N\) there exists an infinite subset \(X\subseteq N\) such that \(f\rceil X\) either is a constant mapping or a one-to-one mapping, is the earliest canonizing partition theorem. We show how from given canonizing partition theorems corresponding theorems for product structures can be established.'' The paper is organized as follows: {\S}1. Finite sets and arithmetic progressions. {\S}2. A general framework for canonizing theorems. {\S}3. Canonization, diversification, and iterated versions for finite vector spaces. {\S}4. Finite geometric Arguesian lattices.
scientific article; zbMATH DE number 3922656