### Boole’s Rings

- The 14th International Workshop on Set Theory in Luminy October 14, 2017 Assaf Rinot
- Virtual large cardinal principles October 12, 2017 Victoria Gitman
- Borel complexity theory and classification problems October 9, 2017 Samuel Coskey
- Dynamics in the Eremenko-Lyubich class October 8, 2017 Dave Sixsmith – I am a mathematician, not a calculator
- The problem with MathML as a web standard (part 4) September 29, 2017 Peter Krautzberger

### Comments on Boole’s Rings

- Comment on Ord is not definably weakly compact by Ali Enayat October 17, 2017 Comments for Joel David Hamkins
- Comment on Virtual large cardinal principles by Victoria Gitman October 16, 2017 Comments for Victoria Gitman
- Comment on Virtual large cardinal principles by Neil Barton October 16, 2017 Comments for Victoria Gitman
- Comment on Square principles by The 14th International Workshop on Set Theory in Luminy | Assaf Rinot October 15, 2017 Comments for Assaf Rinot
- Comment on Math for seven-year-olds: graph coloring, chromatic numbers, and Eulerian paths and circuits by Joel David Hamkins October 10, 2017 Comments for Joel David Hamkins

# Category Archives: Research

## 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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## 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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## 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

Posted in Musings, Research, Talks
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## An incompleteness theorem for β_{n} models

My first paper was “An incompleteness theorem for $\beta_n$ models” with Stephen Simpson [1]. It’s a short paper, but the idea is very pretty. We know that the incompleteness theorem implies there are strange models of arithmetic, but these models … Continue reading

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## The logic of Reverse Mathematics

This post is about a research idea I have been thinking about which is quite different from my usual research. It’s an example of a project with an “old fashioned” feel to it, as if it could have been studied … Continue reading