bio  website  PaulTaylor.EU 

location  London & Birmingham, UK  
age  
visits  member for  5 years, 1 month 
seen  41 mins ago  
stats  profile views  1,863 
I am an independent researcher in the foundations of mathematics and computation, using the techniques of category theory and type theory. I wrote a book called Practical Foundations of Mathematics (CUP 1999). My main work now is Abstract Stone Duality, which seeks to axiomatise computable general topology directly, without any recourse to set theory. I am also the author of a TeX package for drawing categorical diagrams.
6h

comment 
Are all smooth functions composites of 0, 1, and 2ary functions?
Wikipedia is not very informative on (Kolmogorov and) Arnold's work on this topic. Do you have references to (the original papers and) some "popular" account of the ideas that are involved? (The question should perhaps be tagged as real analysis.) 
Jan 29 
awarded  Necromancer 
Jan 29 
revised 
Multiplication of Cauchy and Dedekind real numbers
corrected displayed inequality 
Jan 28 
revised 
Multiplication of Cauchy and Dedekind real numbers
tidying 
Jan 27 
awarded  Revival 
Jan 27 
revised 
Multiplication of Cauchy and Dedekind real numbers
better title, matching the actual difficulty and my answer 
Jan 27 
answered  Multiplication of Cauchy and Dedekind real numbers 
Jan 13 
revised 
Giving $Top(X,Y)$ an appropriate topology
Added PS about Johnstone and in reply to Tyler Lawson, 
Dec 24 
comment 
Is there a notion analogous to separability but requiring definable rather than countable sets?
Besides containing a spelling mistake, your title is misleading about your question. 
Dec 24 
comment 
Is there a notion analogous to separability but requiring definable rather than countable sets?
You're asking that the finite or compact elements of the model be definable. This is one of the requirements for full abstraction; maybe Basil's suggested article by Curien might help you with this. Unfortunately, a lot of the theoretical computer scientists who might have answered this question have now left MathOverflow for another site. 
Dec 20 
awarded  Yearling 
Dec 15 
reviewed  Approve Is there a probability theory developed in intuitionistic logic? 
Dec 15 
revised 
Existence of internal toposes/inner models in a topos
corrected link to my book 
Dec 15 
revised 
Existence of internal toposes/inner models in a topos
added consistency and incompleteness 
Dec 15 
revised 
Existence of internal toposes/inner models in a topos
added link to MO answer on AUs 
Dec 15 
answered  Existence of internal toposes/inner models in a topos 
Dec 14 
comment 
PreOrder induced by continuous functions
I believe that this conjecture is false for reasons of easy real analysis (or order theory). I also consider that the categorical language is obfuscating the problem. (Note that I am a categorist saying this.) 
Dec 14 
comment 
PreOrder induced by continuous functions
I don't follow your notation. If you only have a preorder then it would be better to say glb, inf or meet rather than limit and orderpreserving function rather than functor. Presumably the objects of the preorders are the points of $X$ and you are defining $x\leq_f y$ where $x,y\in X$? The subscripts look confused. What is $R_f$? 
Dec 12 
answered  Can one make a category concrete by “enlarging the universe”? 
Dec 10 
awarded  Synonymizer 