11 citations · 73 across the 28 of their papers we have counts for
23 papers · 1 filter
Loeb Equivalence for General Internal Probability Spaces
Haosui Duanmu, Xinyu Liu, David Schrittesser
Loeb measure theory stands as one of the most influential concepts in nonstandard analysis, underpinning nearly all applications in probability, stochastic processes, and mathemati…
The happy coexistence of mad families and Laver measurability
Asger Tornquist, David Schrittesser
Let denote a Laver real over . We prove that in there is a infinite mad family. Since and sets are Laver measurable in , this shows that…
Maximal eventually different families for uniformly weak Ramsey ideals
Jialiang He, Jintao Luo, David Schrittesser +1
We study -maximal eventually different families of functions from the set of natural numbers into itself where is an arbitrary ideal on the set of natural…
Cofinitary groups and projective well-orders
Vera Fischer, Lukas Schembecker, David Schrittesser
We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks…
Coding over Core Models
Sy David Friedman, Ralf Schindler, David Schrittesser
Early in their careers, both Peter Koepke and Philip Welch made major contributions to two important areas of set theory, core model theory and coding, respectively. In this articl…
Lightface -indescribable cardinals
David Schrittesser
-absoluteness for ccc forcing means that for any ccc forcing , . " inaccessible to reals" means that for any real , ${ω_1}…
Constructing maximal cofinitary groups
David Schrittesser
Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in , that is, without using the Axiom of Choice) maximal cofinitary groups. A…
Maximal discrete sets
David Schrittesser
We survey results regarding the definability and size of maximal discrete sets in analytic hypergraphs. Our main examples include maximal almost disjoint (or mad) families, $\mathc…
Loeb Extension and Loeb Equivalence
Robert M. Anderson, Haosui Duanmu, David Schrittesser +1
In Keisler and Sun (2004), the authors raise several open problems on Loeb equivalences between various internal probability spaces. We provide counter-examples for the first two o…
The Ramsey property and higher dimensional mad families
David Schrittesser, Asger Törnquist
We prove that under a principle of Ramsey regularity there are no infinite maximal almost disjoint families with respect to the transfinitely iterated Fréchet ideals. The results o…
Definable MAD families and forcing axioms
Vera Fischer, David Schrittesser, Thilo Weinert
We show that under the Bounded Proper Forcing Axiom and an anti-large cardinal assumption, there is a MAD family.
Minimal definable graphs of definable chromatic number at least three
Raphael Carroy, Benjamin D. Miller, David Schrittesser +1
We show that there is a Borel graph on a standard Borel space of Borel chromatic number three that admits a Borel homomorphism to every analytic graph on a standard Borel space of…
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…
Good projective witnesses
Vera Fischer, Sy David Friedman, David Schrittesser +1
We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality of a maxima…
A Sacks indestructible co-analytic maximal eventually different family
Vera Fischer, David Schrittesser
In the constructible universe, we construct a co-analytic maximal family of pairwise eventually different functions from to which remains maximal after ad…
Lebesgue's Density Theorem and definable selectors for ideals
Sandra Müller, Philipp Schlicht, David Schrittesser +1
We introduce a notion of density point and prove results analogous to Lebesgue's density theorem for various well-known ideals on Cantor space and Baire space. In fact, we isolate…
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…
Compactness of maximal eventually different families
David Schrittesser
We show that there is an effectively closed maximal eventually different family of functions in spaces of the form for $F\colon \mathbb{N} \to \mathbb{N}\cup\{\mathb…
On Horowitz and Shelah's Borel maximal eventually different family
David Schrittesser
We show there is a closed (in fact effectively closed, i.e., ) eventually different family (working in ZF or less).
Definable discrete sets with large continuum
David Schrittesser
Let be a binary relation and call a set -discrete iff no two distinct of its elements are -related. We show that in the extension of $\…
A co-analytic Cohen indestructible maximal cofinitary group
Vera Fischer, David Schrittesser, Asger Törnquist
Assuming that every set is constructible, we find a maximal cofinitary group of permutations of which is indestructible by Cohen forcing. Thus we show that the…
Definable maximal discrete sets in forcing extensions
David Schrittesser, Asger Törnquist
Let be a binary relation, and recall that a set is -discrete if no two elements of are related by . We show that in the Sacks a…
Projective measure without projective Baire
Sy Friedman, David Schrittesser
We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a set without the Baire property. The…