Mathematical logic; Ian Chiswell; 2007
Mathematical logic; Ian Chiswell; 2007

Mathematical logic

av Ian Chiswell

  • Utgiven: 2007
  • ISBN: 9780199215621
  • Sidor: 260 st
  • Förlag: Oxford University Press
  • Format: Häftad
  • Språk: Engelska

Om boken

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch.Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.

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Mer om Mathematical logic (2007)

2007 släpptes boken Mathematical logic skriven av Ian Chiswell. Den är skriven på engelska och består av 260 sidor. Förlaget bakom boken är Oxford University Press.

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Referera till Mathematical logic

Harvard

Chiswell, I. (2007). Mathematical logic. Oxford University Press.

Oxford

Chiswell, Ian, Mathematical logic (Oxford University Press, 2007).

APA

Chiswell, I. (2007). Mathematical logic. Oxford University Press.

Vancouver

Chiswell I. Mathematical logic. Oxford University Press; 2007.