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Advances in Mathematical Logic
Gaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solu...
Memoirs of a Proof Theorist
This volume is a translation of the book Gödel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K Gödel, Takeuti's personal recollections, and his interpretation of Gödel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic. Contents:On GödelWork of Paul Bernays and Kurt GödelHilbert and GödelShort Biographies of LogiciansSet Theory and Related TopicsFrom Hilbert to GödelAxioms of Arithmetic and Consistency — The Second Problem of HilbertA Report from Gödel '96Having Read “Gödel Remembered”A Tribute to the Memory of Professor Gödel'Appendices:On Gödel's Continuum HypothesisBirth of Second Order Proof Theory by the Fundamental Conjecture on GLC Readership: Those interested in mathematics, especially logic or the history of mathematics. Keywords:Gödel;Logic;Set Theory
Computability and Complexity in Analysis
The workshop on Computability and Complexity in Analysis, CCA 2000, was hosted by the Department of Computer Science of the University of Wales Swansea, September 17{19, 2000. It was the fourth workshop in a successful series of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. About 40 participants from the countries United Kingdom, Germany, Japan, Italy, Russia, France, Denmark, Greece, and Ireland contributed to the success of this meeting. Altogether, 28 talkswere p- sented in Swansea. These proceedings include 23 papers which represent a cro- section through recent research on computability and complexity in analysis. The workshop s...
Proceedings of the 7th & 8th Asian Logic Conferences
The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic.This book contains papers OCo many of them surveys by leading experts OCo of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7th meeting was interrupted by the earthquake in Taiwan and the decision was made to combine the two proceedings. The 8th conference is also the ICM2002 Satellite Conference on Mathematical Logic."
Proceedings of the Sixth Asian Logic Conference
This volume collects written versions of invited and contributed talks presented at the conference. It covers many areas of logic and the foundations of mathematics, as well as computer science. Contents:Seminormal Fine Measures on Pκ(λ) (Y Abe)Effective Baire Category Concepts (K Ambos-Spies & J Reimann)Weak Presentations of Computable Partial Orderings (M M Arslanov & I S Kalimullin)Recursion Theory and Weak Fragments of Peano Arithmetic: A Study of Definable Cuts (C T Chong & Y Yang)Lattice Embedding into d-r.e. Degrees Preserving 0 and 1 (D Ding & L Qian)On Stationary Reflection Principles (Q Feng)Definable Sets of Real Numbers, Infinite Games and Core Model Theory (K Hauser)The Descri...
Proceedings of the 7th and 8th Asian Logic Conferences
The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic. This book contains papers — many of them surveys by leading experts — of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7th meeting was interrupted by the earthquake in Taiwan and the decision was made to combine the...
International e-Conference of Computer Science 2006
Lecture Series on Computer and on Computational Sciences (LSCCS) aims to provide a medium for the publication of new results and developments of high-level research and education in the field of computer and computational science.In this series, only selected proceedings of conferences in all areas of computer science and computational sciences wil
Ethics and Sustainability in Digital Cultures
Digital technologies, now ubiquitous around the world, can promote positive values, as well as support those that are less socially acceptable. To better understand such technologies’ impact on ethics and sustainability, this book situates digital technologies within a cultural context, arguing that the technology is received differently in different cultural contexts. The book contains chapters on state-of-the-art digital technologies such as artificial intelligence from various countries including Japan and Sweden to highlight the multifarious ways in how ethical and sustainability issues are being manifested in certain cultural contexts. The book contributes to furthering understandings...
Words, Languages, and Combinatorics Three
The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography.
