1 citations · 1 across the 4 of their papers we have counts for
8 papers
Manifold classification from the descriptive viewpoint
Jeffrey Bergfalk, Iian B. Smythe
We consider classification problems for manifolds and discrete subgroups of Lie groups from a descriptive set-theoretic point of view. This work is largely foundational in concepti…
A Fraïssé theory for partial orders of a fixed finite dimension
Iian B. Smythe, Mithuna Threz, Max Wiebe
For each , we show that the class of all finite -dimensional partial orders, when expanded with linear orders which realize the partial order, forms a Fraïssé class…
Parametrizing the Ramsey theory of vector spaces I: Discrete spaces
Iian B. Smythe
We show that the Ramsey theory of block sequences in infinite-dimensional discrete vector spaces can be parametrized by perfect sets. As special cases, we prove combinatorial dicho…
Filters on a countable vector space
Iian B. Smythe
We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties…
Mad families of vector subspaces and the smallest nonmeager set of reals
Iian B. Smythe
We show that a parametrized principle, corresponding to the uniformity of the meager ideal, implies that the minimum cardinality of an infinite maximal almost disjoi…
Equivalence of generics
Iian B. Smythe
Given a countable transitive model of set theory and a partial order contained in it, there is a natural countable Borel equivalence relation on generic filters over the model; two…