### Boole’s Rings

- Unifying themes in Ramsey Theory – BIRS 2018 December 3, 2018 Mike Pawliuk – Mathematics
- The rearrangement and subseries numbers: how much convergence suffices for absolute convergence? Mathematics Colloquium, University of Münster, January 2019 November 26, 2018 Joel David Hamkins
- An infinitary-logic-free proof of the Barwise end-extension theorem, with new applications, University of Münster, January 2019 November 26, 2018 Joel David Hamkins
- A new proof of the Barwise extension theorem, without infinitary logic, CUNY Logic Workshop, December 2018 November 26, 2018 Joel David Hamkins
- Preserving Properness November 23, 2018 Asaf Karagila

### Comments on Boole’s Rings

- Comment on The hierarchy of logical expressivity by Stan Letovsky December 9, 2018 Comments for Joel David Hamkins
- Comment on The rearrangement number by The rearrangement and subseries numbers: how much convergence suffices for absolute convergence? Mathematics Colloquium, University of Münster, January 2019 | Joel David Hamkins November 26, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Joel David Hamkins November 9, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Artem Kaznatcheev November 8, 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

# 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