Nonvanishing derived limits from $♣$-type principles

Abstract

Combinatorial set theory provides several tools to study derived limits of certain inverse systems of abelian groups. Most known nonvanishing results for ${\lim }^n$ with $n>1$ depend on some guessing principles of the form $\mathrm{w}◊(S)$ called weak diamonds. In this paper, we explore some applications of the guessing principle $♣(S)$ and its weakenings instead.