### Boole’s Rings

- Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 August 13, 2018 Joel David Hamkins
- Set-theoretic blockchains August 7, 2018 Joel David Hamkins
- Topological models of arithmetic August 6, 2018 Joel David Hamkins
- Real and linear analysis August 1, 2018 Samuel Coskey
- Discrete and foundational mathematics August 1, 2018 Samuel Coskey

### Comments on Boole’s Rings

- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Joel David Hamkins August 15, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Andrej Bauer August 15, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Joel David Hamkins August 13, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by beekmancharlie August 13, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Erin Carmody August 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