### Boole’s Rings

- A countable ordinal definable set of reals without ordinal definable elements January 20, 2017 Victoria Gitman
- Regula Krapf, Ph.D. 2017, University of Bonn January 12, 2017 Joel David Hamkins
- Set-theoretic geology and the downward directed grounds hypothesis, Bonn, January 2017 January 10, 2017 Joel David Hamkins
- My Mathematics Genealogy January 4, 2017 Dana C. Ernst
- Transfinite game values in infinite chess, including new progress, Bonn, January 2017 January 3, 2017 Joel David Hamkins

### Comments on Boole’s Rings

- Comment on A countable ordinal definable set of reals without ordinal definable elements by Victoria Gitman January 21, 2017 Comments for Victoria Gitman
- Comment on A countable ordinal definable set of reals without ordinal definable elements by Robert Solovay January 20, 2017 Comments for Victoria Gitman
- Comment on There are no nondegenerate regular polygons in the integer lattice, except for squares by Joel David Hamkins January 17, 2017 Comments for Joel David Hamkins
- Comment on There are no nondegenerate regular polygons in the integer lattice, except for squares by Pierre B. January 17, 2017 Comments for Joel David Hamkins
- Comment on Math for nine-year-olds: fold, punch and cut for symmetry! by Fold Your Way to Glory – Study Score Calc January 14, 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

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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