Mathematical 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of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material.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covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948.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also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript.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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abbreviated appears applied argument axioms bound brackets C-K ordinal formula calculable called carried Church complete computable consider consists constructive contains conv convertible corresponding defined definition described determined discussion effect equations equivalent example expression extent fact figure finite follows formal function give given Gödel idea interest interpretation introduced intuition kind letters m-configuration machine marked Math mathematical means mechanical method natural numbers normal form notation obtain occur operator ordinal logic particular positive integer possible Practical Forms primitive prints problem programming proof proposition provable prove question recursive reference regarded relation replace represents result rule satisfy scanned sequence squares statement steps substitute suppose symbolic logic symbols term theorem theory tion true Turing Turing's University variables write written