### Boole’s Rings

- Unifying themes in Ramsey Theory – BIRS 2018 December 3, 2018 Mike Pawliuk – Mathematics
- The rearrangement and subseries numbers: how much convergence suffices for absolute convergence? Mathematics Colloquium, University of Münster, January 2019 November 26, 2018 Joel David Hamkins
- An infinitary-logic-free proof of the Barwise end-extension theorem, with new applications, University of Münster, January 2019 November 26, 2018 Joel David Hamkins
- A new proof of the Barwise extension theorem, without infinitary logic, CUNY Logic Workshop, December 2018 November 26, 2018 Joel David Hamkins
- Preserving Properness November 23, 2018 Asaf Karagila

### Comments on Boole’s Rings

- Comment on The hierarchy of logical expressivity by Stan Letovsky December 9, 2018 Comments for Joel David Hamkins
- Comment on The rearrangement number by The rearrangement and subseries numbers: how much convergence suffices for absolute convergence? Mathematics Colloquium, University of Münster, January 2019 | Joel David Hamkins November 26, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Joel David Hamkins November 9, 2018 Comments for Joel David Hamkins
- Comment on Lectures on the Philosophy of Mathematics, Oxford, Michaelmas 2018 by Artem Kaznatcheev November 8, 2018 Comments for Joel David Hamkins
- Comment on Alan Turing, On computable numbers by Joel David Hamkins October 13, 2018 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