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.
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In intuitionistic theories of type theory ( especially higher-type arithmetic ), many forms of the axiom of choice are permitted.
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The Theory of Types and much of Russell's subsequent work have also found practical applications with computer science and information technology.
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{{ quote | 3.331 From this observation we get a further view into Russell's Theory of Types.
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Stephen Kleene in his 1952 " Introduction to Metamathematics " describes the " ramified " theory of types this way:
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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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