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Computable Functions, Logic, and the Foundations of Mathematics
Sofort lieferbar | Lieferzeit: Sofort lieferbar
Artikel-Nr:
9780981550732
Veröffentl:
2018
Seiten:
382
Autor:
Richard L Epstein
eBook Typ:
PDF
eBook Format:
Reflowable
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Beschreibung:
Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
1 Paradoxes2 What Do the Paradoxes Mean?3 Whole Numbers4 Functions5 Proofs6 Infinite Collections?7 Hilbert "On the Infinite"8 Computability9 Turing Machines10 The Most Amazing Fact and Church's Thesis11 Primitive Recursive Functions12 The Grzegorczyk Hierarchy13 Multiple Recursion14 The Least Search Operator15 Partial Recursive Functions16 Numbering the Partial Recursive Functions17 Listability18 Turing Machine Computable = Partial Recursive19 Propositional Logic20 An Overview of First-Order Logic and Gödel's Theorem21 First-Order Arithmetic22 Functions Representable in Formal Arithmetic23 The Undecidability of Arithmetic24 The Unprovability of Consistency25 Church's Thesis26 Constructivist Views of Mathematics27 Mathematics as ModelingComputability and Undecidability—A Timeline