BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Reductions between certain incidence
problems and the Continuum Hypothesis
Samuel Gomes da Silva
UFBA, Brazil
Abstract: We consider two families of incidence problems, C 1 and C 2 ,
which are related to real numbers and countable subsets of the real
line. Instances of problems in C 1 are as follows: given a real number x,
pick randomly a countable set A of reals hoping that x is in A, whereas
instances of problems in C 2 are as follows: given a countable set A of
reals, pick randomly a real number x hoping that x is not in A. One could
arguably defend that, at least intuitively, problems in C 2 are easier to
solve than problems in C 1 . Indeed, we show that, after some suitable
formalization, one can prove (in ZFC) that, on the one hand, problems in
C 2 are at least as simple to solve as problems in C 1 . On the other hand,
the statement “Problems in C 1 have the exact same complexity as
problems in C 2 ” is equivalent to the Continuum Hypothesis.
Date: Thursday 21 March 2019
Time: 16:00
Place: Room S1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
* Enter the University building through the door 20 meters to the right of the main
door and, as you enter the courtyard, turn left, go to the end of the corridor, and
then downstairs.
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 May 30: Logic Fest in the Windy City, Chicago, May 30 – June 2, 2019
 June 19: Boise Extravaganza in Set Theory (BEST) 2019 Conference
 June 26: 12th Young Set Theory Workshop, Vienna, June 26 – 29, 2019
 July 1: 7th European Set Theory Conference, Vienna, July 15, 2019
 July 8: Berkeley conference on inner model theory, July 08–19, 2019
 July 29: Set Theory: Bridging Mathematics and Philosophy, Konstanz, July 2931, 2019
 August 11: Logic Colloquium 2019, Prague, August 11 – 16, 2019
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