7 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…