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Dieter Rödding
Dieter Rödding (24 August 1937 in Hattingen (Ruhr) – 4 June 1984 in Münster) was a German mathematician who main research interest was mathematical logic. Dieter Rödding was born on 24 August 1937 in Hattingen, Ruhr, Germany. In 1956, Rödding began his studies at the Westphalian Wilhelms-University in Münster, Germany. In 1961, he received his doctorate with the dissertation "''Representative sentences about (in the Kalmár-Czillagian sense) elementary functions''", supervised by Gisbert Hasenjaeger. In 1964, he completed his habilitation at Münster with the thesis "''Theory of recursivity over the domain of finite sets of finite rank''". In 1966, he succeeded Hans Hermes as the Chair and Director of the Institute of Mathematical Logic and Fundamental Research at the Westphalian Wilhelms-University, founded by Heinrich Scholz in 1936. Rödding became known through his results on the classification of recursive functions, on recursive types of classical predicate logic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hattingen
Hattingen is a town in the northern part of the Ennepe-Ruhr-Kreis district, in North Rhine-Westphalia, Germany. History Hattingen is located on the south bank of the River Ruhr in the south of the Ruhr region. The town was first mentioned in 1396, when the Duke of Mark granted permission to build a city wall. Today, Hattingen has a picturesque historic district with ''Fachwerk'' (timber-framed houses) built between the 14th and 16th centuries. The old city is still partly surrounded by the city walls today. There are three castles remaining within the municipal area of Hattingen. Historische Stadt- & Ortskerne. Retrieved March 9, 2010 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Mathematical Logic And Fundamental Research
An institute is an organisational body created for a certain purpose. They are often research organisations ( research institutes) created to do research on specific topics, or can also be a professional body. In some countries, institutes can be part of a university or other institutions of higher education, either as a group of departments or an autonomous educational institution without a traditional university status such as a "university institute" (see Institute of Technology). In some countries, such as South Korea and India, private schools are sometimes referred to as institutes, and in Spain, secondary schools are referred to as institutes. Historically, in some countries institutes were educational units imparting vocational training and often incorporating libraries, also known as mechanics' institutes. The word "institute" comes from a Latin word ''institutum'' meaning "facility" or "habit"; from ''instituere'' meaning "build", "create", "raise" or "educate". ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German National Library
The German National Library (DNB; german: Deutsche Nationalbibliothek) is the central archival library and national bibliographic centre for the Federal Republic of Germany. It is one of the largest libraries in the world. Its task is to collect, permanently archive, comprehensively document and record bibliographically all German and German-language publications since 1913, foreign publications about Germany, translations of German works, and the works of German-speaking emigrants published abroad between 1933 and 1945, and to make them available to the public. The DNB is also responsible for the and several special collections like the (German Exile Archive), and the (German Museum of Books and Writing). The German National Library maintains co-operative external relations on a national and international level. For example, it is the leading partner in developing and maintaining bibliographic rules and standards in Germany and plays a significant role in the development of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Problem
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?". The answer is either 'yes' or 'no' depending upon the values of ''x'' and ''y''. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem. A decision procedure for the decision problem "given two numbers ''x'' and ''y'', does ''x'' evenly divide ''y''?" would give the steps for determining whether ''x'' evenly divides ''y''. One such algorithm is long division. If the remainder is zero the answer is 'yes', otherwise it is 'no'. A decision problem which can be solved by an algorithm is called ''decidable''. Decision problems typically appear in mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complexity
Complexity characterises the behaviour of a system or model whose components interaction, interact in multiple ways and follow local rules, leading to nonlinearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. The study of these complex linkages at various scales is the main goal of complex systems theory. The intuitive criterion of complexity can be formulated as follows: a system would be more complex if more parts could be distinguished, and if more connections between them existed. Science takes a number of approaches to characterizing complexity; Zayed ''et al.'' reflect many of these. Neil F. Johnson, Neil Johnson states that "even among scientists, there is no unique definition of complexity – and the scientific notion has traditionally been conveyed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrzej Mostowski
Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma. Biography Born in Lemberg, Austria-Hungary, Mostowski entered University of Warsaw in 1931. He was influenced by Kuratowski, Lindenbaum, and Tarski. His Ph.D. came in 1939, officially directed by Kuratowski but in practice directed by Tarski who was a young lecturer at that time. He became an accountant after the German invasion of Poland but continued working in the Underground Warsaw University. After the Warsaw uprising of 1944, the Nazis tried to put him in a concentration camp. With the help of some Polish nurses, he escaped to a hospital, choosing to take bread with him rather than his notebook containing his research. Some of this research he reconstructed after the War, however much of it remained lost. His work was largely on recursion theory and undecidability. From 1946 until his death in Vancouver, British Columbia, Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Cole Kleene
Stephen Cole Kleene ( ; January 5, 1909 – January 25, 1994) was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism. Biography Kleene was awarded a bachelor's degree from Amherst College in 1930. He was awarded a Ph.D. in mathematics from Princeton University in 1934, where his thesis, entitled ''A Theory of Positi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetical Hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The arithmetical hierarchy is important in recursion theory, effective descriptive set theory, and the study of formal theories such as Peano arithmetic. The Tarski–Kuratowski algorithm provides an easy way to get an upper bound on the classifications assigned to a formula and the set it defines. The hyperarithmetical hierarchy and the analytical hierarchy extend the arithmetical hierarchy to classify additional formulas and sets. The arithmetical hierarchy of formulas The arithmetical hierarchy assigns classifications to the formulas in the language of first-order arithmetic. The classifications are denoted \Sigma^0_n and \Pi^0_n for natural numbers ''n'' (inclu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as in the formula \neg \exists x P(x) which expresses that nothing has the property P. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectrum Of A Theory
In model theory, a branch of mathematical logic, the spectrum of a theory is given by the number of isomorphism classes of models in various cardinalities. More precisely, for any complete theory ''T'' in a language we write ''I''(''T'', ''κ'') for the number of models of ''T'' (up to isomorphism) of cardinality ''κ''. The spectrum problem is to describe the possible behaviors of ''I''(''T'', ''κ'') as a function of ''κ''. It has been almost completely solved for the case of a countable theory ''T''. Early results In this section ''T'' is a countable complete theory and ''κ'' is a cardinal. The Löwenheim–Skolem theorem shows that if ''I''(''T'',''κ'') is nonzero for one infinite cardinal then it is nonzero for all of them. Morley's categoricity theorem was the first main step in solving the spectrum problem: it states that if ''I''(''T'',''κ'') is 1 for some uncountable ''κ'' then it is 1 for all uncountable ''κ''. Robert Vaught showed that ''I''(''T'',ℵ0) canno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
