### Boole’s Rings

- On checking a proof July 24, 2017 Dave Sixsmith
- Second-order transfinite recursion is equivalent to Kelley-Morse set theory over GBC July 23, 2017 Joel David Hamkins
- Nebula-The cryptocurrency that will produce the reversible computer July 22, 2017 Joseph Van Name
- The transitive multiverse July 22, 2017 Asaf Karagila
- The fundamental problem of math on the web July 21, 2017 Peter Krautzberger

### Comments on Boole’s Rings

- Comment on Infinite Combinatorial Topology by Rodrigo Hernández-Gutiérrez July 25, 2017 Comments for Assaf Rinot
- Comment on Open determinacy for class games by Second-order transfinite recursion is equivalent to Kelley-Morse set theory over GBC | Joel David Hamkins July 23, 2017 Comments for Joel David Hamkins
- Comment on Transfinite recursion as a fundamental principle in set theory by Second-order transfinite recursion is equivalent to Kelley-Morse set theory over GBC | Joel David Hamkins July 23, 2017 Comments for Joel David Hamkins
- Comment on Games with the computable-play paradox by Warren D Smith July 21, 2017 Comments for Joel David Hamkins
- Comment on Ordinal definable subsets of singular cardinals by saf July 18, 2017 Comments for Assaf Rinot

# 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