A Concise Introduction to Mathematical LogicSpringer Science & Business Media, 28.09.2006 - 256 Seiten While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. |
Inhalt
Gödels Completeness Theorem | 71 |
The Foundations of Logic Programming | 105 |
Elements of Model Theory | 131 |
Incompleteness and Undecidability | 167 |
On the Theory of SelfReference | 209 |
Hints to the Exercises | 231 |
Literature | 241 |
| 247 | |
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abelian groups algebra applications arbitrary arithmetical axiom system axiomatic axiomatizable axiomatizable theory basic Boolean functions calculus called claim clearly collision-free compactness theorem consistent countable deduction theorem defined definition denoted densely ordered derivable domain elementarily equivalent elementary elements embeddable enumeration equations equivalent example Exercise exists extension finite first-order language formal Gödel Gödel number graph hence holds Horn clauses Horn formulas implies induction hypothesis induction step infinite instance isomorphism K₁ L-structure Lemma logic programming mathematical means model complete n-ary obtain p.r. function p₁ predicate prime formulas proof propositional logic provability logic provable prove quantifier elimination real closed fields recursive rules satisfies sentences sequence set of formulas set theory signature structure subset substructure T-model t₁ tautologies term Theorem 3.1 ultrafilter ultraproducts unary undecidable V-formula valid variables vart verify yields