Boole’s Rings- On conjugacy problems for graphs and trees October 11, 2019 Samuel Coskey
- (with Y. Hayut) Perfect Subtree Property for Weakly Compact Cardinals October 10, 2019 Sandra Müller
- Structural properties of the stable core October 10, 2019 Victoria Gitman
- Ground model definability in ${\rm ZF}$ October 10, 2019 Victoria Gitman
- (with S.-D. Friedman and V. Gitman) Structural Properties of the Stable Core October 4, 2019 Sandra Müller
- Comments on Boole’s Rings
- Comment on Solution to my transfinite epistemic logic puzzle, Cheryl’s Rational Gifts by Cheryl’s Rational Gifts: transfinite epistemic logic puzzle challenge! | Joel David Hamkins October 14, 2019 Comments for Joel David Hamkins
- Comment on The propagation of error in classical geometry constructions by Paul Alberti-Strait October 9, 2019 Comments for Joel David Hamkins
- Comment on The modal logic of arithmetic potentialism and the universal algorithm by The $Sigma_1$-definable universal finite sequence | Joel David Hamkins September 30, 2019 Comments for Joel David Hamkins
- Comment on I know that you know that I know that you know…. Oxford, October 2019 by Joel David Hamkins September 25, 2019 Comments for Joel David Hamkins
- Comment on I know that you know that I know that you know…. Oxford, October 2019 by charlie sitler September 25, 2019 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
Posted in Talks
Leave a comment
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
Posted in Papers, Research
Leave a comment
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
Posted in Musings, Results worth knowing
Leave a comment
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
Posted in Talks, Uncategorized
Leave a comment
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.
Posted in Research, Talks
Leave a comment
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
4 Comments
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
Posted in Research, Talks
3 Comments
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
Posted in Musings, Research, Talks
Leave a comment
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
Posted in Musings
8 Comments
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