### Boole’s Rings

- Bi-interpretation in set theory, Bristol, February 2020 January 22, 2020 Joel David Hamkins
- Fake Reflection January 20, 2020 Assaf Rinot
- Bi-interpretation in weak set theories January 16, 2020 Joel David Hamkins
- A Microscopic approach to Souslin-tree constructions. Part II January 7, 2020 Assaf Rinot
- Philosophy meets maths, Oxford, January 2020 January 7, 2020 Joel David Hamkins

### Comments on Boole’s Rings

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- Comment on A new proof of the Barwise extension theorem, without infinitary logic by The $Sigma_1$-definable universal finite sequence | Joel David Hamkins January 14, 2020 Comments for Joel David Hamkins
- Comment on Lectures on the philosophy of mathematics, Oxford, Michaelmas term 2019 by Joel David Hamkins January 8, 2020 Comments for Joel David Hamkins
- Comment on Lectures on the philosophy of mathematics, Oxford, Michaelmas term 2019 by Klaus Loehnert January 8, 2020 Comments for Joel David Hamkins
- Comment on Climb into Cantor's attic by Joel David Hamkins January 4, 2020 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