Constructivism in Mathematics, Vol 1 Elsevier, 1 lug 1988 - 355 pagine These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature. |
Sommario
| 1 | |
Chapter 2 Logic | 35 |
Chapter 3 Arithmetic | 113 |
Chapter 4 Nonclassical axioms | 185 |
Chapter 5 Real numbers | 251 |
Parole e frasi comuni
A(Sx AC-NN algorithm argument arithmetic assume assumption axioms B₁ bar induction BHK-interpretation Brouwer chapter choice sequences classical logic clauses closure conditions constructive mathematics d₁ defined definitional extension derivable E-logic elements equivalent example exercise existence FAND(T finite formal function symbols fundamental sequences FV(A given hence Heyting intuition intuitionism intuitionistic logic Kleene Kreisel Kripke model language lawlike lemma Markov's principle metamathematical metric space monotone natural deduction natural numbers negative translation node notation notion obtained operations P₁ partial recursive predicate logic prime formulas primitive recursive arithmetic primitive recursive functions proof PROPOSITION Prove quantifiers r₁ real numbers realizability recursion theory rules S₁ satisfying schema soundness theorem Specker sequence subset Suppose t₁ theorem tion tree Troelstra Troelstra 1973 uniformly continuous variables WC-N weak counterexample x₁ xA(x y₁ ΑΛΒ