Mathematica Notebook: Models of Classical Cardinal Characteristics and Open Questions

This notebook is complementary material to the book CCC Forcing Constructions for the Real Line by D. A. Mejía, M. Goldstern, J. Kellner, and S. Shelah. Its goal is to investigate open questions concerning the consistency with ZFC of inequalities of the form y<x, where x and y are classical cardinal characteristics of the continuum.

The notebook encodes the known provable inequalities between characteristics, as a directed graph, and stores information from classical forcing models (such as Cohen, Random, Hechler, Laver, Miller, and others) as assignments of values to the vertices of this graph. A collection of algorithms processes this data to identify potential open questions and unexplored consistency patterns.

The notebook was developed and tested using Wolfram Mathematica 15.0.0. An online version can be accessed from the Wolfram Cloud through the link below (this online version might be updated at some stage in the future). No additional packages are required.

https://www.wolframcloud.com/obj/damejiag/Public/2charmodels.nb

Intended use: the notebook serves as a research and exploration tool accompanying the book, allowing readers and researchers to experiment with the encoded data and generate potential open problems concerning cardinal characteristics of the continuum.