Parallel non-linear iterations

TL;DR

This paper constructs models demonstrating various consistent inequalities among cardinal invariants of the continuum, specifically focusing on non-linear iterations and their impact on these invariants.

Contribution

It introduces a method for parallel non-linear iterations to establish the consistency of complex cardinal invariant configurations.

Findings

Established the consistency of $rak{b}<rak{s}<rak{d}<rak{c}$

Achieved constellations like $rak{b}<rak{r}<rak{d}<rak{c}$, $rak{b}<rak{e}<rak{d}<rak{c}$, and $rak{b}<rak{u}<rak{d}<rak{c}$

Abstract

Developing a system of parallel non-linear iterations, we establish the consistency of $\mathfrak{b}<\mathfrak{s}<\mathfrak{d}<\mathfrak{c}$ where $\mathfrak{b}, \mathfrak{d}, \mathfrak{c}$ are arbitrary subject to the known ZFC restrictions and $\mathfrak{s}$ is regular. By evaluating other invariants we achieve also the constellations $\mathfrak{b}<\mathfrak{r}<\mathfrak{d}<\mathfrak{c}$, $\mathfrak{b}<\mathfrak{e}<\mathfrak{d}<\mathfrak{c}$ and $\mathfrak{b}<\mathfrak{u}<\mathfrak{d}<\mathfrak{c}$.