boolesrings.org

logic.dorais.org

Reverse Mathematics | François G. Dorais

http://logic.dorais.org/topics/reverse-math

François G. Dorais. Mathematical Logic and Foundations. Towsner’s stable forcing. That shows that $ Ind{ Sigma 0 n}$ gives absolutely no control whatsoever on $ Delta 0 {n 1}$-definable sets. Hellip; →. In everyday language, the word. To imply wrongful intent. This can lead to awkward social situations, but what I want to talk about here is how axiom schemes can sometimes behave badly and may lead to awkward mathematical situations. Hellip; →. In a recent paper [ 1. For every coloring (c: N 2 to set{0, d...

logic.dorais.org

Set Theory | François G. Dorais

http://logic.dorais.org/topics/set-theory

François G. Dorais. Mathematical Logic and Foundations. Some time ago, Asaf Karagila wrote wonderful post. Wherein he shows that, even without assuming the axiom of choice one can always find four cardinals ( mathfrak{p} lt mathfrak{q} ). And ( mathfrak{r} lt mathfrak{s} ). Such that ( mathfrak{p} { mathfrak{r} = mathfrak{q} { mathfrak{s} . ). In the comments, Harvey Friedman asks. Your theorem is an example of an existential sentence about cardinals in the language with only ( lt ). Hellip; →. J Symb&#4...

logic.dorais.org

Proof Theory | François G. Dorais

http://logic.dorais.org/topics/proof-theory

François G. Dorais. Mathematical Logic and Foundations. After a productive year at the Institute for Advanced Study, the Univalent Foundations Program has written a book on Homotopy Type Theory. HoTT) The foreword gives a succinct description of the purpose of this book:. Having addressed all the necessary caveats, let’s talk about why this book is interesting and why you should read it…. What is so hot about HoTT? The most interesting aspect from my point of view is that HoTT fully supports. Is actually...

logic.dorais.org

HoTT Math Series | François G. Dorais

http://logic.dorais.org/archives/1448

François G. Dorais. Mathematical Logic and Foundations. I am planning to do a series of posts where I attempt to do math in Homotopy Type Theory (HoTT). The plan is to do some relatively simple proof-relevant mathematics at an informal level. The topics will all be undergraduate level so the mathematics won’t be hard to follow. I’m hoping to keep the series brief so each post will only be an appetizer and not a full course dinner. Enjoy! More on equational logic. Unit group of a ring. You’re right&...

logic.dorais.org

Papers | François G. Dorais

http://logic.dorais.org/papers

François G. Dorais. Mathematical Logic and Foundations. On uniform relationships between combinatorial problems. With D. Dzhafarov, J. Hirst, J. Mileti, P. Shafer. Transactions of the American Mathematical Society 368 (2016), 1321–1359. Comparing the strength of diagonally non-recursive functions in the absence of $ Sigma 0 2$ induction. With J. Hirst, P. Shafer. Journal of Symbolic Logic 80 (2015), 1211–1235. Doi:10.1017/jsl.2015.43. Reverse mathematics of compact countable second-countable spaces.

logic.dorais.org

News | François G. Dorais

http://logic.dorais.org/news

François G. Dorais. Mathematical Logic and Foundations. Even closer to the origin! SMBC on madness…. Back to the origin…. Possibly true. Necessarily funny. XKCD on the Axiom of Choice…. Hello Booles’ Rings! Leave a Reply Cancel reply. Your email address will not be published. Required fields are marked *. Notify me of follow-up comments by email. Notify me of new posts by email. Even closer to the origin! On the structure of universes in HoTT. HoTT Math 4: Local rings and fields. On HoTT Math Series.

peterkrautzberger.org

So that took a while · Peter Krautzberger

https://www.peterkrautzberger.org/0181

Peter Krautzberger on the web. So that took a while. I finally completed the blog migration I started a few months ago. Moving away from WordPress forced me to re-think a few parts and re-work a lot of content by hand. This was tedious but forced a worthwhile bit of introspection. I’ve switched to the simplest permalink structure enumeration. But then the question was: how many digits (I like my numbers to be the same string length)? It’ll be a pain! I’m not a cool indieweb dev. Having to do a lot of man...

logic.dorais.org

Selected Papers Network | François G. Dorais

http://logic.dorais.org/archives/1414

François G. Dorais. Mathematical Logic and Foundations. I just made my first contribution. To the Selected Papers Network. It was fun and easy and I strongly recommend you use it too! It’s too early for serious commentary on the experience but there are a few things I noted right away:. The front page selectedpapers.net. Does not yet support MathJax. Neither does Google but that’s another problem.) Hopefully that will be fixed soon. Meanwhile, you can use the MathJax bookmarklet. I wish topic (hash)tags.

logic.dorais.org

Combinatorics | François G. Dorais

http://logic.dorais.org/topics/combinatorics

François G. Dorais. Mathematical Logic and Foundations. Some time ago, Asaf Karagila wrote wonderful post. Wherein he shows that, even without assuming the axiom of choice one can always find four cardinals ( mathfrak{p} lt mathfrak{q} ). And ( mathfrak{r} lt mathfrak{s} ). Such that ( mathfrak{p} { mathfrak{r} = mathfrak{q} { mathfrak{s} . ). In the comments, Harvey Friedman asks. Your theorem is an example of an existential sentence about cardinals in the language with only ( lt ). Hellip; →. J Symb&#4...