### Boole’s Rings

- Consistency strength lower bounds for the proper forcing axiom via the core model induction March 5, 2020 Sandra Müller
- Logic Colloquium Poznan - TBA March 5, 2020 Sandra Müller
- North American Annual Meeting of the ASL - How to obtain lower bounds in set theory March 4, 2020 Sandra Müller
- International Day of Mathematics, Vienna - Das Unbegreifliche verstehen - die Faszination Unendlichkeit March 3, 2020 Sandra Müller
- The real numbers are not interpretable in the complex field February 24, 2020 Joel David Hamkins

### Comments on Boole’s Rings

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- Comment on Set-theoretic geology by A tutorial in set-theoretic geology, London 2011 | Joel David Hamkins March 21, 2020 Comments for Joel David Hamkins
- Comment on The real numbers are not interpretable in the complex field by Joel David Hamkins March 4, 2020 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