In his published paper on the subject, Dumas introduces his theory of types.
2.
By the time of his 1908 " Mathematical logic as based on the theory of types"
3.
They sought to banish the paradoxes of naive set theory by employing a theory of types they devised for this purpose.
4.
Church's theory of types helped the formal system avoid the Kleene Rosser paradox that afflicted the original untyped lambda calculus.
5.
In intuitionistic theories of type theory ( especially higher-type arithmetic ), many forms of the axiom of choice are permitted.
6.
The Theory of Types and much of Russell's subsequent work have also found practical applications with computer science and information technology.
7.
{{ quote | 3.331 From this observation we get a further view into Russell's Theory of Types.
8.
Stephen Kleene in his 1952 " Introduction to Metamathematics " describes the " ramified " theory of types this way:
9.
Quine dismisses this notion of " bound variable " as " " pointless apart from a certain aspect of the theory of types " ".
10.
Holmes has shown that NFP has the same consistency strength as the predicative theory of types of " Principia Mathematica " without the Axiom of reducibility.
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