Church is better known for the as a result accomplishments: His proof that Peano arithmetic and first order logic are undecidable. A latter symptom is referred to as Church's theorem. His articulation of has are to exist as referred to as Church's thesis. He was a introduction editor of the Journal of Symbolic Logic, editing its reviews subdivision until 1979. His discovery of the lambda calculus.

A lambda calculus emerged in his renowned 1936 paper showing the being of an "undecidable problem". This symptom preempted Alan Turing's famous act on the halting problem which also demonstrated the being of a condition unresolvable by mechanical means. He & Turing so showed that a lambda calculus & a Turing machine used in Turing's halting condition were same inside capabilities, & after demonstrated the kind of guide "mechanical processes for computation" experienced tantamount computational abilities. This resulted in the Church-Turing thesis.

A lambda calculus influenced a project of the LISP programming language and functional programming languages in general. A Church boolean is named within his honor.

Church's doctorial students were an inordinately accomplished lot, including Stephen Kleene, J. Barkley Rosser, Alan Turing, Leon Henkin, John George Kemeny, Martin Davis, Michael O. Rabin, Dana Scott, Raymond Smullyan, and Hartley Rogers, Jr. Watch [http://www.math.ucla.edu/~asl/bsl/0104/0104-005.ps].