Author | Barnes, Donald W. author |
---|---|

Title | An Algebraic Introduction to Mathematical Logic [electronic resource] / by Donald W. Barnes, John M. Mack |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1975 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-4489-7 |

Descript | IX, 123 p. online resource |

SUMMARY

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a subยญ stantial course on abstract algebra. Consequently, our treatment ofthe subยญ ject is algebraic. Although we assurne a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of . the exercises. We also assurne a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model oflogic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based-rather, any conclusions to be drawn about the foundations of mathematics co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory

CONTENT

I Universal Algebra -- II Propositional Calculus -- III Properties of the Propositional Calculus -- IV Predicate Calculus -- V First-Order Mathematics -- VI Zermelo-Fraenkel Set Theory -- VII Ultraproducts -- VIII Non-Standard Models -- IX Turing Machines and Gรถdel Numbers -- X Hilbertโ{128}{153}s Tenth Problem, Word Problems -- References and Further Reading -- Index of Notations

Mathematics
Algebra
Mathematical logic
Mathematics
Mathematical Logic and Foundations
Algebra