Publications with Gabriel Fernandes

2.
Gabriel Fernandes
,
Miguel Moreno
,
Assaf Rinot
,
Fake reflection
. Israel Journal of Mathematics. To appear.

Abstract:
We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection from ZFC, and present applications of filter reflection to the study of canonical equivalence relations over the higher Cantor and Baire spaces.

PDF

arXiv

1.
Gabriel Fernandes
,
Miguel Moreno
,
Assaf Rinot
,
Inclusion modulo nonstationary
. Monatshefte fΓΌr Mathematik (2020) 192: 827  851.

Abstract:
A classical theorem of Hechler asserts that the structure (Ο^Ο,β€^*)is universal in the sense that for any πdirected poset P with no maximal element, there is a ccc forcing extension in which (Ο^Ο,β€^*) contains a cofinal orderisomorphic copy of P. In this paper, we prove a consistency result concerning the universality of the higher analogue (οΈβͺ^βͺ,β€^π)οΈ.


Theorem.
Assume GCH. For every regular uncountable cardinal βͺ, there is a cofinalitypreserving GCHpreserving forcing extension in which for every analytic quasiorder Q over βͺ^βͺ and every stationary subset π of βͺ, there is a Lipschitz map reducing Q to (βͺ^βͺ,β€^π).


PDF

arXiv

Journal