12 citations · 22 across the 13 of their papers we have counts for
16 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…
Higher limits of wider systems
Jeffrey Bergfalk, Matteo Casarosa
Write for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal to the set of nat…
Infinitary combinatorics in condensed math and strong homology
Jeffrey Bergfalk, Chris Lambie-Hanson
Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong ho…
An introduction to higher walks
Jeffrey Bergfalk
The following is an introduction to the study of higher walks, by which we mean a family of higher-dimensional extensions of Todorcevic's method of walks on the ordinals. After a b…
Whitehead's problem and condensed mathematics
Jeffrey Bergfalk, Chris Lambie-Hanson, Jan Šaroch
One of the better-known independence results in general mathematics is Shelah's solution to Whitehead's problem of whether implies that an abelian…
The definable content of homological invariants II: Čech cohomology and homotopy classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebr…
A descriptive approach to higher derived limits
Nathaniel Bannister, Jeffrey Bergfalk, Justin Tatch Moore +1
We present a new aspect of the study of higher derived limits. More precisely, we introduce a complexity measure for the elements of higher derived limits over the directed set …
Simutaneously vanishing higher derived limits without large cardinals
Jeffrey Bergfalk, Michael Hrušák, Chris Lambie-Hanson
A question dating to Sibe Mardešić and Andrei Prasolov's 1988 work Strong homology is not additive, and motivating a considerable amount of set theoretic work in the ensuing years,…
On the additivity of strong homology for locally compact separable metric spaces
Nathaniel Bannister, Jeffrey Bergfalk, Justin Tatch Moore
We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric sp…
The definable content of homological invariants I: &
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the first installment in a series of papers in which we illustrate how classical invariants of homological algebra and algebraic topology can be enriched with additional de…
The first omega alephs: from simplices to trees of trees to higher walks
Jeffrey Bergfalk
The point of departure for the present work is Barry Mitchell's 1972 theorem that the cohomological dimension of is . We record a new proof and mild strengthening o…
Definable (co)homology, pro-torus rigidity, and (co)homological classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
We show that the classical homology theory of Steenrod may be enriched with descriptive set-theoretic information. We prove that the resulting definable homology theory provides a…
Simultaneously vanishing higher derived limits
Jeffrey Bergfalk, Chris Lambie-Hanson
In 1988, Sibe Mardešić and Andrei Prasolov isolated an inverse system with the property that the additivity of strong homology on any class of spaces which includes th…
Ramsey theory for monochromatically well-connected subsets
Jeffrey Bergfalk
We define well-connectedness, an order-theoretic notion of largeness whose associated partition relations formally weaken those of the classical Ramsey relations…
The Cohomology of the Ordinals I: Basic Theory and Consistency Results
Jeffrey Bergfalk, Chris Lambie-Hanson
In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is Čech cohomology. We show i…
Strong Homology, Derived Limits, and Set Theory
Jeffrey Bergfalk
We consider the question of the additivity of strong homology. This entails isolating the set-theoretic content of the higher derived limits of an inverse system indexed by the fun…