## Mathematical LogicMathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists. |

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### Contents

1 | |

Type Theory | 149 |

Enigmas Mysteries and Loose Ends | 223 |

281 | |

Lists of contents of other volumes | 289 |

matters arising from other volumes | 293 |

### Common terms and phrases

A. M. TURING Alan Turing Alonzo Church applied argument Aufz axiom of infinity Bletchley Park brackets C-K ordinal formula Church Church's system circle-free complete configuration computable function computable numbers computable sequence computing machine conv convertible corresponding deduction theorem defined definition described effectively calculable Entscheidungsproblem equivalent expression of index follows formal free variables given Gödel Hilbert Hodges hypothesis idea internal configuration interpretation intuition Kleene letters logic formula m-configuration Math means method n-th natural numbers nested-type system Newman normal form notation noun-class number-theoretic theorems obtain operator ordinal formula representing ordinal logic paper positive integer possible Practical Forms primitive recursive primitive recursive function prints problem programming proof proposition formulas provable equation provable formula prove real number recursive function replace result Robin Gandy rule scanned symbol sequence of symbols squares suppose symbolic logic tape theory of types tion Turing machine Turing's type theory X-definable