6 citations · 6 across the 5 of their papers we have counts for
6 papers · 1 filter
Set theory and a model of the mind in psychology
Asger Törnquist, Jens Mammen
We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called \e…
The Ramsey property implies no mad families
David Schrittesser, Asger Törnquist
We show that if all collections of infinite subsets of have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. This solves a long-standing…
Maximal almost disjoint families, determinacy, and forcing
Karen Bakke Haga, David Schrittesser, Asger Törnquist
We study the notion of -MAD families where is a Borel ideal on . We show that if is an arbitrary ideal, or is any finite or countably…
Projective maximal families of orthogonal measures with large continuum
Vera Fischer, Sy-David Friedman, Asger Tornquist
We study maximal orthogonal families of Borel probability measures on (abbreviated m.o. families) and show that there are generic extensions of the constructible universe …
A co-analytic maximal set of orthogonal measures
Vera Fischer, Asger Tornquist
We prove that if then there is a maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known T…
The Effective Theory of Borel Equivalence Relations
Ekaterina B. Fokina, Sy-David Friedman, Asger Tornquist
The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-L…