### Boole’s Rings

- Some thoughts about teaching introductory courses in set theory September 21, 2017 Asaf Karagila
- The set-theoretic universe is not necessarily a class-forcing extension of HOD September 19, 2017 Joel David Hamkins
- Equivalence relations and classification problems, parts 1 and 2 September 19, 2017 Samuel Coskey
- On the classification of automorphisms of trees September 11, 2017 Samuel Coskey
- The hierarchy of second-order set theories between GBC and KM and beyond September 9, 2017 Joel David Hamkins

### Comments on Boole’s Rings

- Comment on Some thoughts about teaching introductory courses in set theory by Harto Saarinen September 24, 2017 Comments for Asaf Karagila
- Comment on Some thoughts about teaching introductory courses in set theory by Dan Saattrup Nielsen September 23, 2017 Comments for Asaf Karagila
- Comment on Some thoughts about teaching introductory courses in set theory by Joseph Van Name September 22, 2017 Comments for Asaf Karagila
- Comment on Every countable model of set theory embeds into its own constructible universe by Incomparable $omega_1$-like models of set theory | Joel David Hamkins September 19, 2017 Comments for Joel David Hamkins
- Comment on Local properties in set theory by Neil Barton September 18, 2017 Comments for Joel David Hamkins

# Category Archives: Results worth knowing

## An example with Dedekind cuts

In this post, I will briefly describe an example in computability theory that is well known, but not easy to find in the literature. It gives one reason why Dedekind cuts are difficult to work with computationally. Theorem. There is … Continue reading

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## Filter quantifiers

I have been supervising an undergraduate student in an independent study in topology this semester. We have just finished the Stone–Čech compactification, and the semester is ending, so I want to end with an ultrafilter based proof of Hindman’s theorem. … Continue reading

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## Computable roots of computable functions

Here are several interesting results from computable analysis: Theorem 1. If $f$ is a computable function from $\mathbb{R}$ to $\mathbb{R}$ and $\alpha$ is an isolated root of $f$, then $\alpha$ is computable. Corollary 2. If $p(x)$ is a polynomial over … Continue reading