### Boole’s Rings

- A variety of mathematical proof-of-work problems will provide better security for cryptocurrencies than hash-based proof-of-work problems May 24, 2017 Joseph Van Name
- Euclidean Ramsey Theory 2 – Ramsey DocCourse Prague 2016 May 24, 2017 Mike Pawliuk
- Graphs obtained from endomorphic Laver tables May 16, 2017 Joseph Van Name
- Moment of Zen May 16, 2017 Asaf Karagila
- Kaethe Lynn Bruesselbach Minden, PhD 2017, CUNY Graduate Center May 12, 2017 Joel David Hamkins

### Comments on Boole’s Rings

- Comment on A program that accepts exactly any desired finite set, in the right universe by Joel David Hamkins May 26, 2017 Comments for Joel David Hamkins
- Comment on Infinite Combinatorial Topology by saf May 25, 2017 Comments for Assaf Rinot
- Comment on Infinite Combinatorial Topology by Ari Brodsky May 25, 2017 Comments for Assaf Rinot
- Comment on A Microscopic approach to Souslin-tree constructions. Part I by saf May 24, 2017 Comments for Assaf Rinot
- Comment on Math for nine-year-olds: fold, punch and cut for symmetry! by Symmetry – G∞AT May 23, 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