Author Archives: Carl Mummert

Talk: Survey of mathematically applied computability theory

Posted on November 19, 2016 by Carl Mummert

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 →

Posted in Talks | Leave a comment

Reverse Mathematics of Matroids

Posted on April 22, 2016 by Carl Mummert

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 →

Posted in Papers, Research | Leave a comment

An example with Dedekind cuts

Posted on April 19, 2016 by Carl Mummert

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 →

Posted in Musings, Results worth knowing | Leave a comment

Talk on Reverse Mathematics and Ramsey Theory

Posted on March 18, 2016 by Carl Mummert

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 →

Posted in Talks, Uncategorized | Leave a comment

Talk on the existence of connected components of graphs

Posted on September 23, 2015 by Carl Mummert

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.

Posted in Research, Talks | Leave a comment

Filter quantifiers

Posted on November 30, 2014 by Carl Mummert

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 | 4 Comments

Talk on Reverse Mathematics and the Modal Logic of Reverse Mathematics

Posted on November 25, 2013 by Carl Mummert

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 →

Posted in Research, Talks | 3 Comments

Internal combinatorics and uniform reducibility

Posted on December 5, 2012 by Carl Mummert

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 →

Posted in Musings, Research, Talks | Leave a comment

Quiz on public peer review

Posted on April 5, 2012 by Carl Mummert

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 →

Posted in Musings | 8 Comments

Computable roots of computable functions

Posted on February 14, 2012 by Carl Mummert

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 →

Posted in Results worth knowing | Tagged , | 4 Comments