Church's Thesis (constructive Mathematics)
In constructive mathematics, Church's thesis (CT) is an axiom which states that all total functions are computable. The axiom takes its name from the Church–Turing thesis, which states that every effectively calculable function is computable function, but the constructivist version is much stronger, claiming that every function is computable.
The axiom CT is incompatible with classical logic in sufficiently strong systems. For example, Heyting arithmetic (HA) with CT as an addition axiom is able to disprove some instances of the law of the excluded middle. However, Heyting arithmetic is equiconsistent with Peano arithmetic (PA) as well as with Heyting arithmetic plus Church's thesis. That is, adding either the law of the excluded middle or Church's thesis does not make Heyting arithmetic inconsistent, but adding both does.
Read more about Church's Thesis (constructive Mathematics): Formal Statement, Relationship To Classical Logic, Extended Church's Thesis
Famous quotes containing the words church and/or thesis:
“Midnight has come and the great Christ Church bell
And many a lesser bell sound through the room;
And it is All Souls’ Night.
And two long glasses brimmed with muscatel
Bubble upon the table. A ghost may come;
For it is a ghost’s right....”
—William Butler Yeats (1865–1939)
“The average Ph.D. thesis is nothing but a transference of bones from one graveyard to another.”
—J. Frank Dobie (1888–1964)