## A Concise Introduction to Mathematical LogicWhile 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

The Foundations of Logic Programming 4 1 Term Models and Horn Formulas 4 2 Propositional Resolution 4 3 Unification 4 4 Logic Programming ... | 4 |

Elements of Model Theory 5 1 Elementary Extensions 5 2 Complete and κCategorical Theories 5 3 Ehrenfeuchts game 5 4 Embedding and Characte... | 5 |

Incompleteness and Undecidability 6 1 Recursive and Primitive Recursive Functions 6 2 Arithmetization 6 3 Representability of Arithmetical Predicat... | 6 |

On the Theory of SelfReference 7 1 The Derivability Conditions 7 2 The Theorems of Gödel and Löb 7 3 The Provability Logic G 7 4 The Modal T... | 7 |

Hints to the Exercises | 24 |

1 | 33 |

3 | 41 |

### Other editions - View all

### Common terms and phrases

abelian groups algebra application arbitrary arithmetical axiom system axiomatic axiomatizable axiomatizable theory basic Boolean functions calculus called claim clearly collision—free compactness theorem computable conﬁrms consequence relation constant countable deduction theorem deﬁned deﬁnition denoted densely ordered derivable domain elementarily equivalent elementary elements embeddable enumeration equations equivalent example Exercise exists extension ﬁeld finite ﬁrst ﬁxed formal hence holds Horn clauses Horn formulas I-pA IIpA implies induction hypothesis induction step inﬁnite instance isomorphism L-structure Lemma logic program mathematical means model complete obtain operation symbol p.r. function precisely predicate predicate logic prime formulas proof propositional logic provability logic provable prove quantifier elimination recursive rules satisfiable satisﬁes sequence set of formulas signature strings structure subset substitution substructure Suppose T-model tautologies term Theorem 3.1 trivial ultraproducts unary undecidable universal Horn valid variables vart verify yields