Author | Monk, J. Donald. author |
---|---|

Title | Mathematical Logic [electronic resource] / by J. Donald Monk |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1976 |

Connect to | http://dx.doi.org/10.1007/978-1-4684-9452-5 |

Descript | X, 532 p. online resource |

SUMMARY

From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book

CONTENT

Interdependence of sections -- I Recursive Function Theory -- I. Turing machines -- 2. Elementary recursive and primitive recursive functions -- 3. Recursive functions; Turing computability -- 4. Markov algorithms -- 5. Recursion theory -- 6. Recursively enumerable sets -- 7. Survey of recursion theory -- II Elements of Logic -- 8. Sentential logic -- 9. Boolean algebra -- 10. Syntactics of first-order languages -- 11. Some basic results of first-order logic -- 12. Cylindric algebras -- III Decidable and Undecidable Theories -- 13. Some decidable theories -- 14. Implicit definability in number theories -- 15. General theory of undecidability -- 16. Some undecidable theories -- 17. Unprovability of consistency -- IV Model Theory -- 18. Construction of models -- 19. Elementary equivalence -- 20. Nonstandard mathematics -- 21. Complete theories -- 22. The interpolation theorem -- 23. Generalized products -- 24. Equational logic -- 25. Preservation and characterization theorems -- 26. Elementary classes and elementary equivalence -- 27. Types -- 28. Saturated structures -- V Unusual Logics -- 29. Inessential variations -- 30. Finitary extensions -- 31. Infinitary extensions -- Index of symbols -- Index of names and definitions

Mathematics
Mathematical logic
Mathematics
Mathematical Logic and Foundations