Logic and StructureSpringer Science & Business Media, 2004 - 263 páginas From the reviews: "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts of mathematics. The reader immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary TOC:Introduction.- Propositional Logic.- Predicate Logic.- Completeness and Applications.- Second Order Logic.- Intuitionistic Logic.- Normalisation.- Goedel's Theorem.- Bibliography.- Index.- |
Conteúdo
Introduction | 2 |
Predicate Logic | 57 |
Completeness and Applications | 103 |
Second Order Logic | 143 |
Intuitionistic Logic | 153 |
Normalisation | 187 |
Gödels theorem | 209 |
| 257 | |
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Termos e frases comuns
algebra apply arithmetic atoms axiomatizable axioms called cardinality Completeness Theorem computation connectives consider constant symbols construction contains Contradiction Corollary defined definition disjunction elements elimination equivalence example Exercise finite first-order first-order logic formula free variables function symbols Gödel hence Induction hypothesis infinite input introduce intuitionistic logic k₁ Kripke model language Lemma mathematics maximally consistent Mod(T natural deduction natural numbers node non-standard model normal form notation Note notion occur ordered set partial recursive functions partially ordered predicate logic predicate symbol prenex prime primitive recursive functions Proof PROP properties propositional logic Prov provable prove quantifier reader recursion theory relation rule second-order logic semantics sentences Show Skolem function structures subformula subset substitution Suppose t₁ theory truth table valuation Vx(x Vxy(x xx(x xy(x σ σ واح