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Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding.Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics.ContributorsScott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

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Hrsg. vom Deutschen Archäologischen Institut. Mit Beiträgen von Curtis L. Clay, Alan Cameron und Pierre Lardet. Aus dem Inhalt: Die Kontorniaten als Quelle der Stadtrömischen Geschichte im 4. und 5. Jahrhundert n. Chr. Die Ikonographie einiger Kontorniaten-Vorderseiten. Die Ikonographie der Kontorniaten-Rückseiten. Die Beizeichen der Kontorniaten. Die neuzeitlichen Fälschungen der Kontorniaten. Addenda zum Katalog (AMuGS; Band VI.1). Register. Die Texte beinhalten auch die vom Verfasser am Ende seines Lebens noch für gültig gehaltenen Teile seines Werkes von 1943, zum Teil in überarbeiteter Form. XXIII,455 Seiten und 64 Tafeln, Großformat, Leinen (Antike Münzen und geschnittene Steine; Band VI.2/Walter de Gruyter 1990) leicht angeschmutzt. Statt EUR 209,00. Gewicht: 2430 g - Gebunden/Gebundene Ausgabe - Sprache: Deutsch

"The book is nothing short of a tour de force and should be required reading for landscape urbanists and landscape architects. Students and general audiences of design and planning will find it difficult to go back into their disciplinary silos."-Alan Berger, MIT "Combinatory Urbanism delves into armatures and manouvers which is what an urban mechanism-a city-is made up of. Looking at structure, not style, Mayne actually inhabits style-if we redefine the word to suggest invention engaging with logic. In so doing, he creates new categories of 'place'."-Peter Cook "Mayne has produced a powerful view of how an architect can re-envision the city. Combinatory Urbanism is not just an architect's summary of his latest or greatest projects, but a true challenge to all of us in the design community-to think differently, challenge the norms, and seek new ground in the form of open collaborations for re-envisioning the city."-Philip Enquist, SOM "The Swiss build the Gottard tunnel; the Chinese move the Yellow River; the Koreans suggest connecting the Han and the Nakdong; and someone whispers re-build the Mississippi Delta. Combinatory Architecture is Combinatory Urbanism: colossal scale; sophisticated technique; re-imagined environments; re-invented sociologies. Mayne's collective form points the circuitous way."-Eric Moss, Director, SCI-Arc "Not since Urbanisme or Learning from Las Vegas have the stakes for urban design been raised so quickly and so high."-Albert Pope, Rice University "Combinatory Urbanism is a perfect example of why Mayne continues to stay on the cutting edge of architecture and urban planning. Educators and students alike should take note of Mayne's innovative approach to creating a more sustainable, just, economically productive society."-Jeremy Rifkin, The Foundation on Economic Trends

"The book is nothing short of a tour de force and should be required reading for landscape urbanists and landscape architects. Students and general audiences of design and planning will find it difficult to go back into their disciplinary silos."-Alan Berger, MIT "Combinatory Urbanism delves into armatures and manouvers which is what an urban mechanism-a city-is made up of. Looking at structure, not style, Mayne actually inhabits style-if we redefine the word to suggest invention engaging with logic. In so doing, he creates new categories of 'place'."-Peter Cook "Mayne has produced a powerful view of how an architect can re-envision the city. Combinatory Urbanism is not just an architect's summary of his latest or greatest projects, but a true challenge to all of us in the design community-to think differently, challenge the norms, and seek new ground in the form of open collaborations for re-envisioning the city."-Philip Enquist, SOM "The Swiss build the Gottard tunnel; the Chinese move the Yellow River; the Koreans suggest connecting the Han and the Nakdong; and someone whispers re-build the Mississippi Delta. Combinatory Architecture is Combinatory Urbanism: colossal scale; sophisticated technique; re-imagined environments; re-invented sociologies. Mayne's collective form points the circuitous way."-Eric Moss, Director, SCI-Arc "Not since Urbanisme or Learning from Las Vegas have the stakes for urban design been raised so quickly and so high."-Albert Pope, Rice University "Combinatory Urbanism is a perfect example of why Mayne continues to stay on the cutting edge of architecture and urban planning. Educators and students alike should take note of Mayne's innovative approach to creating a more sustainable, just, economically productive society."-Jeremy Rifkin, The Foundation on Economic Trends