The Five WH’s of Set Theory

I was asked to write a short introduction to set theory for the European Set Theory Society website. I attempted to give a short answer to what is set theory, why study it, when and how to study it and where to find resources.

You can find the article on the ESTS’ website “Resources” page, or in the Papers section of my website.

My goal was to present set theory in general, and $\ZF$-centric in particular. But I also included class set theories, atoms and non-well founded theories, as well as New Foundations, and an ending paragraph that points into additional directions (like categories or type theory) and philosophical questions (which should promptly be discussed over beer).

I initially tried to include references for $\ETCS$ or constructive set theories like $\mathsf{IZF}$ or $\mathsf{CZF}$. But I’m not familiar with references to these subjects, and the text began to grow longer than I had hoped. So those were omitted at the end.

In any case, feel free to leave me a comment, or an email, or a note attached to a beer, with your critique or opinion on this article.

3 thoughts on “The Five WH’s of Set Theory”

  1. Certainly Tom Leinster’s AMM article (arXiv link: is a decent first skim of and gentle approach to the ideas of structural set theory, but given the task, I don’t blame you for not wanting to open up another whole approach to set theory on your readers without decent references/discussion.

    1. That, and I specifically didn’t like that article very much (as witnessed by my blog post about it from the days of yore). :-)

      But you are right. I mostly tried to be brief, and I felt that adding another entirely different approach would be a bit too much.

      1. I know it wasn’t your favourite, but worth a pointer to readers here perhaps. More technical but also very thorough from both sides is Mike Shulman’s comparison of material and structural set theories, the first half (roughly) of

        I didn’t say above, but I think the note is a very useful reference!

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