17 citations · 51 across the 17 of their papers we have counts for
15 papers · 1 filter
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…
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…
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…
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…