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.

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

Abstract: A classical theorem of Hechler asserts that the structure (ω^ω,≤^*)is universal in the sense that for any 𝜎directed poset P with no maximal element, there is a ccc forcing extension in which (ω^ω,≤^*) contains a cofinal orderisomorphic copy of P. In this paper, we prove a consistency result concerning the universality of the higher analogue (︀K^K,≤^𝑆)︀.


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


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