## A Tour Through Mathematical Logic, Volume 30The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gödel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject. |

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### Contents

Calculus of Variations by G A Bliss out of print | 1 |

Analytic Functions of a Complex Variable by D R Curtiss out of print | 2 |

Mathematical Statistics by H L Rietz out of print | 3 |

Projective Geometry by J W Young out of print | 4 |

A History of Mathematics in America before 1900 by D E Smith and Jekuthiel Ginsburg out of print | 5 |

Fourier Series and Orthogonal Polynomials by Dunham Jackson out of print | 6 |

Vectors and Matrices by C C MacDuffee out of print | 7 |

Kings and Ideals by N H McCoy out of print | 8 |

Knot Theory by Charles Livingston | 24 |

Homomorphisms in the Service of Geometry by Sherman Stein and Sandor Szabo | 25 |

The Sensual Quadratic Form by John H Conway assisted by Francis Y C Fung | 26 |

A Panorama of Harmonic Analysis by Steven G Krantz | 27 |

Inequalities from Complex Analysis by John P DAngelo | 28 |

Ergodic Theory of Numbers by Karma Dajani and Cor Kraaikamp | 29 |

A Tour through Mathematical Logic by Robert S Wolf | 30 |

MAA Service Center P O Box 91112 | 52 |

The Theory of Algebraic Numbers second edition by Harry Pollard and Harold G Diamond | 9 |

The Arithmetic Theory of Quadratic Forms by B W Jones out of print | 10 |

Irrational Numbers by Ivan Niven | 11 |

Statistical Independence in Probability Analysis and Number Theory by Mark | 12 |

A Primer of Real Functions third edition by Ralph P Boas | 13 |

Combinatorial Mathematics by Herbert J Ryser | 14 |

Noncommutative Kings by I N Herstein | 15 |

Dedekind Sums by Hans Rademacher and Emil Grosswald | 16 |

The Schwarz Function and Its Applications by Philip J Davis | 17 |

Celestial Mechanics by Harry Pollard | 18 |

Field Theory and Its Classical Problems by Charles Robert Hadlock | 19 |

The Generalized Kiemann Integral by Robert M McLeod | 20 |

From ErrorCorrecting Codes through Sphere Packings to Simple Groups by Thomas M Thompson | 21 |

Random Walks and Electric Networks by Peter G Doyle and J Laurie Snell | 22 |

The Geometric Viewpoint by Steven G Krantz | 23 |

Axiomatic Set Theory | 59 |

Recursion Theory and Computability | 95 |

Godels Incompleteness Theorems | 135 |

Model Theory | 165 |

Contemporary Set Theory | 225 |

Nonstandard Analysis | 279 |

Constructive Mathematics | 317 |

A A Deductive System for Firstorder Logic | 347 |

Cardinal Arithmetic | 355 |

Groups Rings and Fields | 361 |

375 | |

Symbols and Notation | 381 |

387 | |

### Other editions - View all

A Tour through Mathematical Logic: A Real Analysis Approach Robert S. Wolf No preview available - 2010 |

### Common terms and phrases

algebraic assume axiom of choice axiomatizable basic bijection binary relation Borel Brouwer calculus called Cantor Chapter compactness complete consistent constant symbol constructive Corollary countable defined definition denote denumerable domain element example Exercise existence finite number first-order language first-order logic first-order theory formal formula free variables func function symbols Godel number hierarchy Hilbert implies important incompleteness theorem induction infinite input integer interval isomorphic large cardinal lemma mathematicians means model theory natural number nonempty nonstandard notation notion ordered field ordinal partial recursive Peano arithmetic polynomial PR function predicate prenex form proof proper axioms propositional logic provable prove quantifier-free real numbers real-closed recursive function relation symbol ring rule of inference second-order logic Section sentence sequence set of real set theory Skolem statement structure tion true truth table Turing machine uncountable upper bound usual