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Martin Löb
Martin Hugo Löb (; 31 March 1921 – 21 August 2006) was a German mathematician. He settled in the United Kingdom after the Second World War and specialised in mathematical logic. He moved to the Netherlands in the 1970s, where he remained in retirement. He is perhaps best known for having formulated Löb's theorem in 1955. Early life and education Löb grew up in Berlin, but escaped from the Third Reich, arriving in the UK just before the outbreak of the Second World War. As an enemy alien, he was deported on the ''Dunera'' to an internment camp at Hay in Australia in 1940, where the 19-year-old Löb was taught mathematics by other internees. His teacher, Felix Behrend, was later a professor at Melbourne University. Löb was allowed to return to the UK in 1943, and he studied at the University of London after the War. After graduating, he became a research student with Reuben Goodstein at the University of Leicester. He completed his PhD and became an assistant lecturer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Australia
Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, smaller islands. With an area of , Australia is the largest country by area in Oceania and the world's List of countries and dependencies by area, sixth-largest country. Australia is the oldest, flattest, and driest inhabited continent, with the least fertile soils. It is a Megadiverse countries, megadiverse country, and its size gives it a wide variety of landscapes and climates, with Deserts of Australia, deserts in the centre, tropical Forests of Australia, rainforests in the north-east, and List of mountains in Australia, mountain ranges in the south-east. The ancestors of Aboriginal Australians began arriving from south east Asia approximately Early human migrations#Nearby Oceania, 65,000 years ago, during the Last Glacial Period, last i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Löb's Paradox
Curry's paradox is a paradox in which an arbitrary claim ''F'' is proved from the mere existence of a sentence ''C'' that says of itself "If ''C'', then ''F''", requiring only a few apparently innocuous logical deduction rules. Since ''F'' is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic. The paradox is named after the logician Haskell Curry. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem. In natural language Claims of the form "if A, then B" are called conditional claims. Curry's paradox uses a particular kind of self-referential conditional sentence, as demonstrated in this example: Even though Germany does not border China, the example sentence certainly is a natural-language sentence, and so the truth of that sentence can be analyzed. The pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents Mathematical proof, proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as Recursive data type, inductively-defined data structures such as list (computer science), lists, boxed lists, or Tree (data structure), trees, which are constructed according to the axioms and rule of inference, rules of inference of the logical system. Consequently, proof theory is syntax (logic), syntactic in nature, in contrast to model theory, which is Formal semantics (logic), semantic in nature. Some of the major areas of proof theory include structural proof theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word "professor" is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well. This usage would be considered incorrect among other academic communities. However, the otherwise unqualified title "Professor" designated with a capital let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reader (academic Rank)
The title of reader in the United Kingdom and some universities in the Commonwealth of Nations, for example India, Australia and New Zealand, denotes an appointment for a senior academic with a distinguished international reputation in research or scholarship. In the traditional hierarchy of British and other Commonwealth universities, reader (and principal lecturer in the new universities) are academic ranks above senior lecturer and below professor, recognising a distinguished record of original research. Reader is similar to a professor without a chair, similar to the distinction between ''professor extraordinarius'' and ''professor ordinarius'' at some European universities, professor and chaired professor in Hong Kong and "professor name" (or associate professor) and chaired professor in Ireland. Readers and professors in the UK would correspond to full professors in the United States.Graham WebbMaking the most of appraisal: career and professional development planning for le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Leeds
, mottoeng = And knowledge will be increased , established = 1831 – Leeds School of Medicine1874 – Yorkshire College of Science1884 - Yorkshire College1887 – affiliated to the federal Victoria University1904 – University of Leeds , type = Public , endowment = £90.5 million , budget = £751.7 million , chancellor = Jane Francis , vice_chancellor = Simone Buitendijk , students = () , undergrad = () , postgrad = () , city = Leeds , province = West Yorkshire , country = England , campus = Urban, suburban , free_label = Newspaper , free = The Gryphon , colours = , website www.leeds.ac.uk, logo = Leeds University logo.svg , logo_size = 250 , administrative_staff = 9,200 , coor = , affiliations = The University of Leeds is a public research university in Leeds, West Yorkshire, England. It was established in 1874 as the Yorkshire College of Science. In 1884 it merged with the Leeds School of Medicine (established 1831) and was renam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common Academic degree, degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title ''Doctor (title), Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Leicester
, mottoeng = So that they may have life , established = , type = public research university , endowment = £20.0 million , budget = £326 million , chancellor = David Willetts , vice_chancellor = Nishan Canagarajah , head_label = Visitor , head = The King , academic_staff = 1,705 (2018/19) , administrative_staff = 2,205 (2018/19) , students = () , undergrad = () , postgrad = () , city = Leicester , country = England, UK , coordinates = , campus = Urban parkland , colours = , website = , logo = UniOfLeicesterLogo.svg , logo_size = 250px , affiliations = ACUAMBA EMUA EUA Sutton 30 M5 UniversitiesUniversities UK The University of Leicester ( ) is a public research university based in Leicester, England. The main campus is south of the city centre, adjacent to Victoria Park. The university's predecessor, University College, Leicester, gained university status in 1957. The university had an income of £323.1 million in 2019/20, of which £5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
