Andrew Brooke-Taylor's Research Page
My main area of interest is in set theory, specifically, large cardinal
axioms and forcing.
I am also very interested in connections between set theory and other
fields of mathematics, especially category theory and algebraic topology,
which I studied before switching to set theory.
Large cardinal axioms are axioms that extend
the usual (ZFC) axioms for set theory, strengthening the theory.
Forcing is the standard technique for proving consistency results for other
set-theoretic principles; put them together and you can address interesting
questions about which strengthenings of ZFC are compatible with
which other set-theoretic principles.
Subcompact cardinals, squares, and stationary reflection.
Israel Journal of Mathematics (2013). DOI: 10.1007/s11856-013-0007-x
Indestructibility of Vopenka's Principle,
Archive for Mathematical Logic 50, no. 5 (2011) , pp 515-529.
With Sy-David Friedman.
Large cardinals and gap-1 morasses,
Annals of Pure and Applied Logic 159, no. 1-2 (2009), pp 71-99.
Large cardinals and definable well-orders on the universe,
Journal of Symbolic Logic 74, no. 2 (June 2009) pp 641-654.
My Doctoral Thesis:
Large Cardinals and L-like Combinatorics
For a bit of light relief, I included a couple
of figures (PS format).
Unprepared Indestructibility (conference paper surveying
"Indestructibility of Vopenka's Principle", above).
RIMS Ko-kyu-roku 1790 (2012), pp 65-71.
Small u_kappa and large 2^kappa for supercompact kappa.
There is a significant literature using large cardinal axioms,
especially Vopenka's Principle, in the study of
locally presentable and accessible categories.
Joan Bagaria and I have been working to advance the area making use
of our set-theoretic perspective. We have already been able to extend
a colimit preservation theorem of Rosicky, Trnkova and Adamek, and
to simplify the
proof of another colimit preservation theorem of Rosicky.
With Joan Bagaria. On colimits and elementary embeddings.
Journal of Symbolic Logic 78 no. 2 (2013), pp 562-578.
Damiano Testa I have done some work on the Fraisse limit of the
class of finite simpicial complexes, and similar structures
for infinite languages which behave in a "locally finite" manner.
In particular we were able to show that there is a 0-1 law in this case,
distinct from the known one due to Blass and Harary (it uses
a different measure on the set of n-vertex simplicial complexes).
However, it has recently come
to our attention that the framework we developed for this is very similar to the
existing one of "parametric classes", so we are reworking
the paper in light of this previous work.
We also show that the geometric realisation of the
Fraisse limit of simplicial complexes is homeomorphic to the infinite simplex
(see the first set of talk slides).
With Damiano Testa. Fraisse limits for infinite relational languages.
I have worked with
Benedikt Loewe and
on the Bousfield lattice in algebraic topology, and with
on rank-to-rank embeddings and their implications for
left self-distributive systems, but don't yet have anything to link to for
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Last updated: 15/5/13 ([d]d/[m]m/yy)