Elements of intuitionism
This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism.
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INTRODUCTORY REMARKS l
ELEMENTARY INTUITIONISTIC MATHEMATICS
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applied arithmetic assert assume atomic formula Axiom of Choice axiom schema b s a Bar Induction basic sequent Beth trees Brouwer's canonical proof choice sequences Church's Thesis classical logic condition consider constructive functions Continuity Principle counter-example decidable defined definition derived determined domain dual sequence dual tree effective element equivalent extensional fact Fan Theorem finite sequences follows formal given Harrop formula hence Heyting lattice holds induction hypothesis infinite initial segment intuitionism intuitionistic logic intuitionistic mathematics intuitive Kripke trees lawless sequences Lemma logical constants mathe mathematical statements means ment natural numbers node obtain operation path platonistic PO-space premiss primitive recursive proof tree-trunk proof-tree provable prove quantifiers real number realizability refutation restriction rules of inference satisfies semantics sentence sentence-letter sentential logic species suppose theory topological Troelstra truth-value valid valuation system verified vertex Vn a(n Vx A(x Vx Fx yield