2,913 reputation
823
bio website PaulTaylor.EU
location London & Birmingham, UK
age
visits member for 5 years, 1 month
seen 41 mins ago

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 2-ary 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 Pre-Order 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 Pre-Order 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 order-preserving 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