7 citations · 11 across the 10 of their papers we have counts for
10 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…
Madness in vector spaces
Iian B. Smythe
We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite…
A local Ramsey theory for block sequences
Iian B. Smythe
We develop local forms of Ramsey-theoretic dichotomies for block sequences in infinite-dimensional vector spaces, analogous to Mathias' selective coideal form of Silver's theorem f…
Borel equivalence relations in the space of bounded operators
Iian B. Smythe
We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten -class, and modulo compact. Us…
Decompositions of the automorphism group of a locally compact abelian group
Iian B. Smythe
It is well known that every locally compact abelian group L can be decomposed as L_1 \oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decompositio…