The $\pi$-Base community database of topological counterexamples was recognized in Fall 2025 as the highest-voted crowdsourced math project on Terence Tao’s MathOverflow list. While much can be done by simply modeling Objects/Spaces, Properties, and Theorems, without a notion of set theory and cardinality, we quickly find limitations, for example:

• Several “open questions” on $\pi$-Base are equivalent to the Continuum Hypothesis
• Thirteen properties on $\pi$-Base are just different cardinalities, with explicit theorems written to connect them.

We will discuss the current plan to incorporate results from set theory into the $\pi$-Base, and seek input from potential users.

Slides for this talk.

Speaker’s website.