Logic & Set Theory seminar: Some algebraic equivalent forms of "all reals are constructible"
Howard House 4th floor seminar room
In 2012 Törnquist and Weiss proved many natural Σ12 definable counterparts of classical equivalences to the Continuum Hypothesis (CH). These become equivalent to “all reals are constructible”. Following this scheme, we proved definable counterparts for some algebraic equivalent form of CH. More specifically we mainly focus on the Σ12 counterpart of a famous result by Erdős and Kakutani: CH holds if and only if the set of all real numbers can be decomposed into countably many subsets, each consisting only of rationally independent numbers.
Organiser: Andrew Brooke-Taylor