Descripción del título
Kurt Gödel [The Princeton ...
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.
Monografía
monografia Rebiun34640788 https://catalogo.rebiun.org/rebiun/record/Rebiun34640788 DE-He213 cr nn 008mamaa 231220s2021 sz | s |||| 0|eng d 9783030872960 978-3-030-87296-0 10.1007/978-3-030-87296-0 doi UR0542211 UR PBX bicssc MAT015000 bisacsh PBX thema 510.9 23 Kurt Gödel electronic resource] The Princeton Lectures on Intuitionism edited by Maria Hämeen-Anttila, Jan von Plato. 1st ed. 2021 Cham Springer International Publishing Imprint: Springer 2021. Cham Cham Springer International Publishing Imprint: Springer IX, 133 p. online resource. IX, 133 p. Text txt rdacontent] computer c rdamedia] online resource cr rdacarrier] text file PDF rda Sources and Studies in the History of Mathematics and Physical Sciences 2196-8829 Gödel's Functional Interpretation in Context -- Part I: Axiomatic Intuitionist Logic -- Part II: The Functional Interpretation -- References -- Name Index. Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy. Mathematics. History. Logic. PhilosophyâHistory. History of Mathematical Sciences. Logic. History of Philosophy. Hämeen-Anttila, Maria. editor. edt. http://id.loc.gov/vocabulary/relators/edt von Plato, Jan. editor. edt. http://id.loc.gov/vocabulary/relators/edt SpringerLink (Online service) Springer Nature eBook Springer Nature eBook Printed edition 9783030872953 Printed edition 9783030872977 Printed edition 9783030872984 Sources and Studies in the History of Mathematics and Physical Sciences 2196-8829.