### Boole’s Rings

- Cohen's Oddity October 20, 2018 Asaf Karagila
- The Stable Core October 15, 2018 Victoria Gitman
- On splitting families October 12, 2018 Samuel Coskey
- MSc thesis on matrix completion October 5, 2018 Nick Gill
- Souslin trees at successors of regular cardinals October 1, 2018 Assaf Rinot

### Comments on Boole’s Rings

- Comment on Alan Turing, On computable numbers by Joel David Hamkins October 13, 2018 Comments for Joel David Hamkins
- Comment on Alan Turing, On computable numbers by Lorenzo Cocco October 13, 2018 Comments for Joel David Hamkins
- Comment on Alan Turing, On computable numbers by Joel David Hamkins October 13, 2018 Comments for Joel David Hamkins
- Comment on Alan Turing, On computable numbers by Sam Butchart October 13, 2018 Comments for Joel David Hamkins
- Comment on Alan Turing, On computable numbers by Joel David Hamkins October 9, 2018 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