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Books > Humanities > Philosophy > Topics in philosophy > Logic
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Mathematical Logic (Hardcover)
Loot Price: R4,853
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Mathematical Logic (Hardcover)
Series: Oxford Texts in Logic
Expected to ship within 12 - 17 working days
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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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