17 citations · 51 across the 17 of their papers we have counts for
18 papers
A free two-generated left distributive algebra of elementary embeddings
Andrew D. Brooke-Taylor, Scott Cramer, Sheila K. Miller Edwards
The set-theoretic large cardinal axiom known as I3 posits the existence of a non-trivial rank-to-rank embedding from an initial segment of the universe of sets into itself. Laver s…
Products of CW complexes
Andrew D. Brooke-Taylor
CW complexes are used extensively in algebraic topology, but the product of two CW complexes need not be a CW complex, as shown by Dowker. Whilst Whitehead and Milnor gave sufficie…
Invariant universality for quandles and fields
Andrew D. Brooke-Taylor, Filippo Calderoni, Sheila K. Miller
We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are…
Inhabitants of interesting subsets of the Bousfield lattice
Andrew Brooke-Taylor, Benedikt Löwe, Birgit Richter
The set of Bousfield classes has some important subsets such as the distributive lattice of all classes which are smash idempotent and the complete…
Cichon's Diagram for uncountable cardinals
Joerg Brendle, Andrew Brooke-Taylor, Sy-David Friedman +1
We develop a version of Cichon's diagram for cardinal invariants on the generalized Cantor space 2^kappa or the generalized Baire space kappa^kappa where kappa is an uncountable re…
The quandary of quandles: The Borel completeness of a knot invariant
Andrew D. Brooke-Taylor, Sheila K. Miller
The isomorphism type of the knot quandle introduced by Joyce is a complete invariant of tame knots. Whether two quandles are isomorphic is in practice difficult to determine; we sh…
Cardinal characteristics at κ in a small u(κ) model
A. D. Brooke-Taylor, V. Fischer, S. D. Friedman +1
We provide a model where u(κ) < 2^κ for a supercompact cardinal κ. Garti and Shelah have provided a sketch of how to obtain such a model by modifying the construction in a paper of…
Accessible images revisited
Andrew Brooke-Taylor, Jiří Rosický
We extend and improve the result of Makkai and Paré that the powerful image of any accessible functor F is accessible, assuming there exists a sufficiently large strongly compact c…
A variant proof of Con(b<a)
Jörg Brendle, Andrew D. Brooke-Taylor
We present a variation of the proof in the first author's "Mob families and mad families" of Con(b<a), which in particular removes some of the obstacles to generalising the argumen…
An analogy between cardinal characteristics and highness properties of oracles
Jörg Brendle, Andrew Brooke-Taylor, Keng Meng Ng +1
We present an analogy between cardinal characteristics from set theory and highness properties from computability theory, which specify a sense in which a Turing oracle is computat…
The infinite random simplicial complex
Andrew Brooke-Taylor, Damiano Testa
We study the Fraisse limit of the class of all finite simplicial complexes. Whilst the natural model-theoretic setting for this class uses an infinite language, a range of results…
Small u_kappa and large 2^kappa for supercompact kappa
Andrew D. Brooke-Taylor
In a recent preprint, Garti and Shelah state that the techniques of a paper of Dzamonja and Shelah can be used to force u_kappa to be kappa^+ for supercompact kappa with 2^kappa ar…
Unprepared Indestructibility
Andrew Brooke-Taylor
This article is based on the talk of the same name which I gave at the "Aspects of Descriptive Set Theory" RIMS Symposium in Kyoto in October 2011; it is essentially just a survey…
On colimits and elementary embeddings
Joan Bagaria, Andrew Brooke-Taylor
We give a sharper version of a theorem of Rosicky, Trnkova and Adamek, and a new proof of a theorem of Rosicky, both about colimit preservation between categories of structures. Un…
Subcompact cardinals, squares, and stationary reflection
Andrew D. Brooke-Taylor, Sy-David Friedman
We generalise Jensen's result on the incompatibility of subcompactness with square. We show that alpha^+-subcompactness of some cardinal less than or equal to alpha precludes squar…
Indestructibility of Vopenka's Principle
Andrew D. Brooke-Taylor
We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need f…
Large cardinals and gap-1 morasses
Andrew D. Brooke-Taylor, Sy-David Friedman
We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obta…
Large Cardinals and Definable Well-Orderings of the Universe
Andrew D. Brooke-Taylor
We use a reverse Easton forcing iteration to obtain a universe with a definable well-ordering, while preserving the GCH and proper classes of a variety of very large cardinals. Thi…