Tim Button

About Open Set Theory

Open Set Theory is a brief introduction to the philosophy of set theory. It is written for students with a little background in logic (such as one might get from forallx:Cambridge), and some high school mathematics. By the end of this book, students reading it might have a sense of:

  1. why set theory came about;
  2. how to reduce large swathes of mathematics to set theory + arithmetic;
  3. how to embed arithmetic in set theory;
  4. what the cumulative iterative conception of set amounts to;
  5. how one might try to justify the axioms of ZFC.
Chapters 1–3 of this book are taken from Open Logic Text, with only tiny changes. Reciprocally, I am contributing Open Set Theory back to the Open Logic Project.

Given the license, you can print as many copies of this as you like, or use the source code to make derivative works, provided you respect various conditions. But if you do use Open Set Theory, please let me know! I can be contacted at tecb2 at cam dot ac dot uk. Equally, and especially since this is a first release, there are guaranteed to be mistakes in this book; if you spot any, please, let me know.

Available downloads

Open Set Theory pdf
Open Set Theory LaTeX source code

About the license

Open Set Theory is released under a Creative Commons license (CC BY 4.0; full details are available here). The following is a human-readable summary of (and not a substitute for) that license. You are free to:
   Share: copy and redistribute the material in any medium or format
   Adapt: remix, transform, and build upon the material for any purpose, even commercially.
Under the following terms:
   Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

Version history

2019
First release; license Creative Commons BY 4.0

Last modified 21 Jan 2019