The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.

With help from his uncle also named Alonzo Church he was able to attend the Ridgefield School for Boys in Ridgefield Connecticut. Church and Turing then showed that the lambda calculus and the Turing machine used in Turing's halting problem were equivalent in capabilities and subsequently demonstrated a variety of alternative "mechanical processes for computation. Anthony Anderson and Michael Zelëny editors Logic Meaning and Computation: Essays in Memory of Alonzo Church (ISBN 978-1-4020-0141-3)


See also

Church–Turing–Deutsch principle
Higher-order logic
Universal set


Notes.

Alonzo Church (June 14 1903 – August 11 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science.