### Boole’s Rings

- What a long strange trip it’s been… April 25, 2017 Asaf Karagila
- The MacLane class and the Eremenko–Lyubich class April 21, 2017 Dave Sixsmith
- The inclusion relations of the countable models of set theory are all isomorphic April 17, 2017 Joel David Hamkins
- All countable models of set theory have the same inclusion relation up to isomorphism, CUNY Logic Workshop, April 2017 April 13, 2017 Joel David Hamkins
- The definable cut of a model of set theory can be changed by small forcing April 10, 2017 Joel David Hamkins

### Comments on Boole’s Rings

- What a long strange trip it’s been… April 25, 2017 Asaf Karagila
- Comment on The inclusion relations of the countable models of set theory are all isomorphic by All countable models of set theory have the same inclusion relation up to isomorphism, CUNY Logic Workshop, April 2017 | Joel David Hamkins April 17, 2017 Comments for Joel David Hamkins
- Comment on Set-theoretic mereology by The inclusion relations of the countable models of set theory are all isomorphic | Joel David Hamkins April 17, 2017 Comments for Joel David Hamkins
- Comment on Set-theoretic mereology by The countable models of set theory all have isomorphic inclusion relations, CUNY Logic Workshop, April 2017 | Joel David Hamkins April 13, 2017 Comments for Joel David Hamkins
- Comment on The definable cut of a model of set theory can be changed by small forcing by Joel David Hamkins April 11, 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