A dichotomy theorem for subsets of the power set of the natural numbers

摘要

The following dichotomy is established for any pair F, G of hereditary families of finite subsets of N : Given N, an infinite subset of N, there exists M an infinite subset of N so that either G boolean AND [M] infinity> subset of F, or F boolean AND [M] infinity>subset of G, where [M] < denotes the set of all finite subsets of M. [References: 18]