Constructivism in Mathematics, Vol 1

כריכה קדמית
Elsevier, 1 ביולי 1988 - 355 עמודים

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.

 

עמודים נבחרים

תוכן

Chapter 1 Introduction
1
Chapter 2 Logic
35
Chapter 3 Arithmetic
113
Chapter 4 Nonclassical axioms
185
Chapter 5 Real numbers
251
Chapter 6 Some elementary analysis
291
Bibliography
327
Index
i
List of symbols
xi
זכויות יוצרים

מונחים וביטויים נפוצים

A V B A(Sx AC-NN algorithm apply 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 equivalent example exercise existence 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 Math metamathematical metric space monotone natural deduction natural numbers negative translation node notation notion obtained operations partial recursive predicate logic prime formulas primitive recursive functions proof PROPOSITION propositional logic Prove quantifiers real numbers realizability recursion theory rules satisfying schema soundness theorem Specker sequence Suppose t₁ t₂ theorem tion tree Troelstra Troelstra 1973 uniformly continuous variables WC-N weak counterexample רר

מידע ביבליוגרפי

כותרתConstructivism in Mathematics, Vol 1
מאתA.S. Troelstra, D. van Dalen
הוצאהElsevier, 1988
ISBN0080570887, 9780080570884
אורך355 עמודים
  
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