### 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

# 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

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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