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François G. Dorais | Mathematical Logic & FoundationsMathematical Logic & Foundations
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Mathematical Logic & Foundations
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François G. Dorais | Mathematical Logic & Foundations | logic.dorais.org Reviews
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Mathematical Logic & Foundations
logic.dorais.org
HoTT Math 4: Local rings and fields | François G. Dorais
http://logic.dorais.org/archives/1517
François G. Dorais. Mathematical Logic and Foundations. HoTT Math 4: Local rings and fields. It’s been a while since the last edition of HoTT Math. Fall is always very busy for me and I’ve been composing this installment one ( varepsilon ). At a time… We are finally arriving at our destination: fields! The main issue with fields is to correctly handle the implicit negation in the term. Since the natural logic of HoTT is intuitionistic rather than classical, this is much more subtle than one would expect.
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...
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...
Posts | François G. Dorais
http://logic.dorais.org/topics
François G. Dorais. Mathematical Logic and Foundations. Even closer to the origin! On the structure of universes in HoTT. HoTT Math 4: Local rings and fields. HoTT Math 3: Unit group of a ring. HoTT Math 2: More on equational logic. HoTT Math 1: Elementary group theory. What is combinatorial set theory? Arithmetical consequences of the set-theoretic multiverse. Towsner’s stable forcing. SMBC on madness…. Back to the origin…. Possibly true. Necessarily funny. A partition theorem for finite trees.
HoTT Math 2: More on equational logic | François G. Dorais
http://logic.dorais.org/archives/1476
François G. Dorais. Mathematical Logic and Foundations. HoTT Math 2: More on equational logic. Last time, I promised we would look at fields. I have to delay this by one or two installments of HoTT Math since there is so much to say and I am struggling to keep these short. This edition of HoTT Math is a continuation of the first. The main lesson of HoTT Math 1. Is a sequence ( sigma ). Of sets indexed by natural numbers. The elements of the set ( sigma n ). Are intended to be symbols for (n ). Can be str...
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Booles' Rings - About
http://boolesrings.org/about
A network of academics. A place for researchers to connect with one another. A place for researchers to share our work and experiences. A test case for the modern researcher home page. Currently, most researchers use their academic homepages for little more than to display contact information and publication lists. We believe it is our responsibility to take charge of our online presence, especially the academic side of it. François G. Dorais.
Ioanna M. Dimitriou Henríquez | Logic, Mathematics, Common Lisp
http://boolesrings.org/ioanna
Ioanna M. Dimitriou Henríquez. Welcome to my page! I am a logician, a mathematician, and a software engineer. In logic and mathematics I’m interested in fomalising set theoretic techniques, and my pet software project is the Choiceless Grapher. Which is written in Common Lisp/Graphviz/bash. I welcome all questions on anything I wrote. Or might know about, and I am always happy to get comments, suggestions, and corrections. 1998-2003). I then went to the ILLC. In Amsterdam for my master’s in Logic. Formal...
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François G. Dorais | Mathematical Logic & Foundations
François G. Dorais. Mathematical Logic and Foundations. Welcome to my research site! Below, you will find of the main research topics I’m interested in. Click on your favorite topic to see what I have to say about it…. In each topic, you will find a variety of posts which usually fall into two types:. Maybe you already read it, in which case you can add your own connections and tidbits of information in the comments…. In that case, we should start a research project together…. François G. Dorais.
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