arXiv subjects

Fabiana Castiblanco

Publications and source records attributed to Fabiana Castiblanco.

3 recordsLinked to original sources

arXiv2021

Preserving levels of projective determinacy by tree forcings

We prove that various classical tree forcings -- for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing -- preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes classes are added to thin projective transitive relations by these forcings.

math.LO↗

arXiv2018

A model with everything except for a well-ordering of the reals

We construct a model of $\mathsf{ZF} + \mathsf{DC}$ containing a Luzin set, a Sierpiński set, as well as a Burstin basis but in which there is no a well ordering of the continuum.

math.LO↗

arXiv2018

When is a real generic over $L$?

In this paper we isolate a new criterion for when a given real $x$ is generic over $L$ in terms of $x$'s capability of lifting elementary embeddings of initial segments of $L$.

math.LO↗