Continuous models of computation : from computability to complexity

A further introduction to forcing I,II Grégory Lafitte & Laurent Bienvenu The method of forcing was introduced by Paul Cohen in 1963 to prove the independence of the Continuum Hypothesis from the Zermelo-Fraenkel axioms of set theory. Following Boban Veličković’s tutorial at the 2015 edition of the Journées Calculabilités, this tutorial will aim at giving a further introduction to the method of forcing. After recalling the fundamental notions introduced in the 2015 tutorial, the core of this two-part tutorial will be a detailed presentation of the various forcing notions, from the classical/historical forcing notions to applications in computability.