### 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

# Author Archives: Carl Mummert

## Talk: Survey of mathematically applied computability theory

Despite being relatively small, my department has three faculty in finite combinatorics, in addition to having me in logic. I recently gave a series of two talks in our seminar to present a broad overview of classical computability theory, and … Continue reading

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## Reverse Mathematics of Matroids

This post is about the paper Reverse Mathematics of Matroids by Jeff Hirst and me. We look at basis theorems for countable vector spaces, countable graphs, and countable enumerated matroids. These three kinds of structures turn out to be extremely … Continue reading

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## 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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## Talk on Reverse Mathematics and Ramsey Theory

This is a copy of my notes from a two-hour talk I gave at our local combinatorics seminar about Reverse Mathematics and Ramsey Theory. The audience consisted of our combinatorialists, who are not logicians, and so the talk is intended … Continue reading

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## Talk on the existence of connected components of graphs

This week I am attending a seminar at Dagstuhl on Measuring the Complexity of Computational Content: Weihrauch Reducibility and Reverse Analysis. This post has slides from my talk and some blog-only remarks to expand on them.

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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

Posted in Results worth knowing
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## Talk on Reverse Mathematics and the Modal Logic of Reverse Mathematics

This is a transcription of notes from a talk I gave on November 1, 2013 to the interdisciplinary logic seminar at the University of Connecticut. I gave a general introduction to Reverse Mathematics and then spoke about my work with … Continue reading

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## Internal combinatorics and uniform reducibility

This post is a set of notes from a talk I gave on December 5th for the discrete mathematics seminar at Marshall University. I want to argue that logical analysis can reveal the “internal combinatorics” of theorems, using some recent … Continue reading

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## Quiz on public peer review

I have been required to complete a “responsible conduct of research” training module by the research office at my school. The reason I am commenting is that I was asked to answer the following question “true” or “false”. This is … 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