6 citations · 17 across the 7 of their papers we have counts for
9 papers
Inner mantles and iterated HOD
Jonas Reitz, Kameryn J Williams
We present a class forcing notion , uniformly definable for ordinals , which forces the ground model to be the -th inner mantle of the extension, in which the s…
Cohen Forcing and Inner Models
Jonas Reitz
Given an inner model and a regular cardinal , we consider two alternatives for adding a subset to by forcing: the Cohen poset , and the Cohen poset o…
The set-theoretic universe is not necessarily a class-forcing extension of HOD
Joel David Hamkins, Jonas Reitz
In light of the celebrated theorem of Vopěnka (1972), proving in ZFC that every set is generic over HOD, it is natural to inquire whether the set-theoretic universe must be a c…
Inner-model reflection principles
Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs +3
We introduce and consider the inner-model reflection principle, which asserts that whenever a statement in the first-order language of set theory is true in the set-theoreti…
From geometry to geology: An invitation to mathematical pluralism through the phenomenon of independence
Jonas Reitz
This paper explores how a pluralist view can arise in a natural way out of the day-to-day practice of modern set theory. By contrast, the widely accepted orthodox view is that ther…
Set-Theoretic Geology
Gunter Fuchs, Joel David Hamkins, Jonas Reitz
A ground of the universe V is a transitive proper class W subset V, such that W is a model of ZFC and V is obtained by set forcing over W, so that V = W[G] for some W-generic filte…