### Boole’s Rings

- Consistency strength lower bounds for the proper forcing axiom via the core model induction March 5, 2020 Sandra Müller
- Logic Colloquium Poznan - TBA March 5, 2020 Sandra Müller
- North American Annual Meeting of the ASL - How to obtain lower bounds in set theory March 4, 2020 Sandra Müller
- International Day of Mathematics, Vienna - Das Unbegreifliche verstehen - die Faszination Unendlichkeit March 3, 2020 Sandra Müller
- The real numbers are not interpretable in the complex field February 24, 2020 Joel David Hamkins

### Comments on Boole’s Rings

- Comment on Math for eight-year-olds: graph theory for kids! by graph theory for children - Oxford Blog March 28, 2020 Comments for Joel David Hamkins
- Comment on Math for seven-year-olds: graph coloring, chromatic numbers, and Eulerian paths and circuits by graph theory for children - Oxford Blog March 28, 2020 Comments for Joel David Hamkins
- Comment on Math for kids: fun with orthoprojections! by Marco March 27, 2020 Comments for Joel David Hamkins
- Comment on Set-theoretic geology by A tutorial in set-theoretic geology, London 2011 | Joel David Hamkins March 21, 2020 Comments for Joel David Hamkins
- Comment on The real numbers are not interpretable in the complex field by Joel David Hamkins March 4, 2020 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

Posted in Papers, Research
Leave a comment

## 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.

Posted in Research, Talks
Leave a comment

## 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
3 Comments

## 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
Leave a comment

## 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
2 Comments

## 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