### 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 HernÃ¡ndez-GutiÃ©rrez 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

# 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

Posted in Research, Talks
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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