8 citations · 20 across the 15 of their papers we have counts for
15 papers · 1 filter
On Absoluteness Between V and HOD
Gabriel Goldberg, Dan Hathaway
We put together Woodin's basis theorem of AD and Vopěnka's theorem to conclude the following: If there is a proper class of Woodin cardinals, then every $(Σ^2_1)^{\mbox…
Classes of barren extensions
Natasha Dobrinen, Daniel Hathaway
Henle, Mathias, and Woodin proved that, provided that holds in a model of ZF, then forcing with over adds no new sets of ordinals,…
Generic Coding with Help and Amalgamation Failure
Sy-David Friedman, Dan Hathaway
We show that if is a countable transitive model of ZF and if are reals not in , then there is a generic over such that . We then present several…
Applying Generic Coding with Help to Uniformizations
Dan Hathaway
This is a follow up to a paper by the author where the disjointness relation for (the graphs of) definable functions from to is analyzed. In that paper, for each $a…
Ramsey Theory on Generalized Baire Space
Dan Hathaway
We show that although the Galvin-Prikry Theorem does not hold on generalized Baire space with the standard topology, there are similar theorems which do hold on generalized Baire s…
Sacks Forcing and the Shrink Wrapping Property
Osvaldo Guzmán González, Dan Hathaway
We consider a property stronger than the Sacks property, called the shrink wrapping property, which holds between the ground model and each Sacks forcing extension. Unlike the Sack…
Perfect Tree Forcings for Singular Cardinals
Natasha Dobrinen, Dan Hathaway, Karel Prikry
We investigate forcing properties of perfect tree forcings defined by Prikry to answer a question of Solovay in the late 1960's regarding first failures of distributivity. Given a…
Forcing and the Halpern-Läuchli Theorem
Natasha Dobrinen, Dan Hathaway
We investigate the effects of various forcings on several forms of the Halpern-Läuchli Theorem. For inaccessible , we show they are preserved by forcings of size less than .…
The Halpern-Läuchli Theorem at a Measurable Cardinal
Natasha Dobrinen, Dan Hathaway
Several variants of the Halpern-Läuchli Theorem for trees of uncountable height are investigated. For weakly compact, we prove that the various statements are all equivalent. W…
Bounding 2D Functions by Products of 1D Functions
François Dorais, Dan Hathaway
Given sets and a regular cardinal , let be the statement that for any function , there are functions and s…
No Unwanted Universally Baire Morphisms
Dan Hathaway
We show that the usual proof that there are no morphisms (in the sense of cardinal characteristics), whose constituent maps are Borel, between certain challenge-response relations…
Combinatorics of reductions between equivalence relations
Dan Hathaway, Scott Schneider
We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions f…
Weak Distributivity Implying Distributivity
Dan Hathaway
Let be a complete Boolean algebra. We show, as an application of a previous result of the author, that if is an infinite cardinal and is weakly $(λ^ω,…
Disjoint Borel Functions
Dan Hathaway
For each , we define a Borel function which encodes in a certain sense. We show that for each Borel $g : \mathbb{R} \to \mat…
A Lower Bound for Generalized Dominating Numbers
Dan Hathaway
We show a new proof for the fact that when and are infinite cardinals satisfying , the cofinality of the set of all functions from to ordered by everywhere…