### Boole’s Rings

- Generalizations of Laver tables Abridged posted! March 21, 2017 Joseph Van Name
- Stationary preserving permutations are the identity on a club March 20, 2017 Asaf Karagila
- Ternary Laver table calculator (now with a local and a global calculator) March 16, 2017 Joseph Van Name
- overlay journals March 16, 2017 Peter Krautzberger
- Computable processes which produce any desired output in the right nonstandard model March 15, 2017 Victoria Gitman

### Comments on Boole’s Rings

- Comment on All triangles are isosceles by Joel David Hamkins March 13, 2017 Comments for Joel David Hamkins
- Comment on All triangles are isosceles by Spring Beauty (@SpringBeautyDJ) March 12, 2017 Comments for Joel David Hamkins
- Comment on All triangles are isosceles by Joel David Hamkins March 11, 2017 Comments for Joel David Hamkins
- Comment on Buckets of fish! by Buckets of Fish and Defeating Hydras | Mike's Math Page March 11, 2017 Comments for Joel David Hamkins
- Comment on All triangles are isosceles by Spring Beauty (@SpringBeautyDJ) March 11, 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

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

Posted in Papers, Research
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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