Titlebook: Higher-Order Computability; John Longley,Dag Normann Book 2015 Springer-Verlag Berlin Heidelberg 2015 Computability Models.Computability T

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978-3-662-51711-6Springer-Verlag Berlin Heidelberg 2015

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https://doi.org/10.1007/978-3-662-47992-6Computability Models; Computability Theory; Intensional Models; Kleene Computability; Lambda Algebras

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John Longley,Dag NormannValuable for researchers in mathematical logic and theoretical computer science.Consolidates work carried out in this domain since the 1950s.Asks what ‘computability’ means for data more complex than

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Theory and Applications of Computabilityhttp://image.papertrans.cn/h/image/426992.jpg

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Introduction and Motivationson computations whose inputs and outputs consisted of . data, such as natural numbers or finite strings of symbols over a finite alphabet, but in this book we shall mainly be concerned with what ‘computability’ might mean for data of a more complex, dynamic kind.

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Some Intensional Modelsram on page 33). This has culminated in Chapters 10 and 11 with the study of the two type structures PC and SR that represent . notions of computable functional subject to certain constraints (Theorems 10.5.7 and 11.3.3).

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Theory of Computability ModelsWe now begin the formal development of our material. Our purpose in this chapter is to set up the general framework within which we shall work, consolidating on the notions of computability model, simulation and equivalence as outlined in Section 1.1, and introducing several important examples.

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The Total Continuous FunctionalsIn this chapter and the next, we turn our attention again to type structures of . functionals over N. From the point of view of computability theory, by far the most important such structure is the model Ct of ., which forms the subject of the present chapter.

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