<P> In set theory, the method of forcing revolutionized the field by providing a robust method for constructing models and obtaining independence results . Paul Cohen introduced this method in 1963 to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo--Fraenkel set theory . His technique, which was simplified and extended soon after its introduction, has since been applied to many other problems in all areas of mathematical logic . </P> <P> Computability theory had its roots in the work of Turing, Church, Kleene, and Post in the 1930s and 40s . It developed into a study of abstract computability, which became known as recursion theory . The priority method, discovered independently by Albert Muchnik and Richard Friedberg in the 1950s, led to major advances in the understanding of the degrees of unsolvability and related structures . Research into higher - order computability theory demonstrated its connections to set theory . The fields of constructive analysis and computable analysis were developed to study the effective content of classical mathematical theorems; these in turn inspired the program of reverse mathematics . A separate branch of computability theory, computational complexity theory, was also characterized in logical terms as a result of investigations into descriptive complexity . </P> <P> Model theory applies the methods of mathematical logic to study models of particular mathematical theories . Alfred Tarski published much pioneering work in the field, which is named after a series of papers he published under the title Contributions to the theory of models . In the 1960s, Abraham Robinson used model - theoretic techniques to develop calculus and analysis based on infinitesimals, a problem that first had been proposed by Leibniz . </P> <P> In proof theory, the relationship between classical mathematics and intuitionistic mathematics was clarified via tools such as the realizability method invented by Georg Kreisel and Gödel's Dialectica interpretation . This work inspired the contemporary area of proof mining . The Curry - Howard correspondence emerged as a deep analogy between logic and computation, including a correspondence between systems of natural deduction and typed lambda calculi used in computer science . As a result, research into this class of formal systems began to address both logical and computational aspects; this area of research came to be known as modern type theory . Advances were also made in ordinal analysis and the study of independence results in arithmetic such as the Paris--Harrington theorem . </P>

Who talked about logic and reason and what was their method