<*logic*>
If we start with a small number of intuitively
computable functions, and
a small number of operations that create new computable functions
from
old
ones, then we can generate a large set of functions
called recursive
functions. If we pick the initial functions and
building operations
so as to
capture what we take to be all the intuitively computable
functions,
then we
generate a set with the same extension as the set of
Turing-computable
functions. (This led Church to conjecture - Church's thesis -
that all intuitively
computable
functions or effective methods are recursive functions.)
Recursive
function
theory studies these functions, their method of generation,
ways to
prove
that some functions are not recursive in this sense, and related
matters.

[Glossary of First-Order Logic]

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