The Continuum Problem, or Hilbert's first problem, asks whether the Continuum Hypothesis is true. It's arguably the most famous unsolved
problem from Hilbert's list. In this talk, I'll present recent progress made in set theory related to the Continuum Problem.
I'll point out the metamathematical significance of the Continuum Hypothesis through a
stunning theorem of Hugh Woodin which roughly states that the Continuum Hypothesis is a universal \Sigma^2_1 statement for generic absoluteness. If time permits, I'll talk about \Omega-logic, a strong logic used to analyze truth in the structure (H(\omega_2), \in) which could settle the Continuum Problem.