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Martin Goldstern
Martin Goldstern (born 7 May 1963 in Austria) is an Austrian mathematician and university professor for set theory at the TU Wien and head of thresearch unit 1of thInstitute of Discrete Mathematics and Geometry His main research lies in set theory of the real line and forcing theory, and applications of set theory in universal algebra. He is cousin of Martin Karplus and great-nephew of Eugenie Goldstern. Academic career Goldstern earned a Ph.D. in 1986 at the TU Wien under the direction of Robert F. Tichy, with a dissertation in equidistribution; and another in set theory in 1991 at UC Berkeley under the direction of Jack Silver and Haim Judah. As postdoc he held temporary positions at Bar Ilan University, Freie Universität Berlin and Carnegie Mellon University. He acquired habilitation at TU Wien in 1993 with the thesis ''Tools for your forcing construction'', which greatly simplified, and made widely accessible, a general preservation theorem of Saharon Shelah for countab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austria
Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous city and state. A landlocked country, Austria is bordered by Germany to the northwest, the Czech Republic to the north, Slovakia to the northeast, Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the west. The country occupies an area of and has a population of 9 million. Austria emerged from the remnants of the Eastern and Hungarian March at the end of the first millennium. Originally a margraviate of Bavaria, it developed into a duchy of the Holy Roman Empire in 1156 and was later made an archduchy in 1453. In the 16th century, Vienna began serving as the empire's administrative capital and Austria thus became the heartland of the Habsburg monarchy. After the dissolution of the H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Forcing
In the mathematical field of set theory, the proper forcing axiom (''PFA'') is a significant strengthening of Martin's axiom, where forcings with the countable chain condition (ccc) are replaced by proper forcings. Statement A forcing or partially ordered set P is proper if for all regular uncountable cardinals \lambda , forcing with P preserves stationary subsets of lambda\omega . The proper forcing axiom asserts that if P is proper and Dα is a dense subset of P for each α<ω1, then there is a filter G P such that Dα ∩ G is nonempty for all α<ω1. The class of proper forcings, to which PFA can be applied, is rather large. For example, standard arguments show that if P is or [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theorists
Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electronics and computing *Set (abstract data type), a data type in computer science that is a collection of unique values ** Set (C++), a set implementation in the C++ Standard Library * Set (command), a command for setting values of environment variables in Unix and Microsoft operating-systems * Secure Electronic Transaction, a standard protocol for securing credit card transactions over insecure networks * Single-electron transistor, a device to amplify currents in nanoelectronics * Single-ended triode, a type of electronic amplifier * Set!, a programming syntax in the scheme programming language Biology and psychology * Set (psychology), a set of expectations which shapes perception or thought *Set or sett, a badger's den *Set, a small tuber ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Austrian Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austrian Logicians
Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Austrian German dialect * Something associated with the country Austria, for example: ** Austria-Hungary ** Austrian Airlines (AUA) ** Austrian cuisine ** Austrian Empire ** Austrian monarchy ** Austrian German (language/dialects) ** Austrian literature ** Austrian nationality law ** Austrian Service Abroad ** Music of Austria ** Austrian School of Economics * Economists of the Austrian school of economic thought * The Austrian Attack variation of the Pirc Defence chess opening. See also * * * Austria (other) * Australian (other) Australian(s) may refer to: Australia * Australia, a country * Australians, citizens of the Commonwealth of Australia ** European Australians ** Anglo-Celtic Australians, Australians descended principally from British colonists ** Aboriginal Au ... * L'Autrichienne (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The European Mathematical Society
'' Journal of the European Mathematical Society'' is a monthly peer-reviewed mathematical journal. Founded in 1999, the journal publishes articles on all areas of pure and applied mathematics. Most published articles are original research articles but the journal also publishes survey articles.Summary of the journal The journal has been published by until 2003. Since 2004, it is published by the . The first editor-in-chief was |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems are two theorems of mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ... that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistency, consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra Universalis
''Algebra Universalis'' is an international scientific journal focused on universal algebra and lattice theory. The journal, founded in 1971 by George Grätzer, is currently published by Springer-Verlag. Honorary editors in chief of the journal included Alfred Tarski and Bjarni Jónsson Bjarni Jónsson (February 15, 1920 – September 30, 2016) was an Icelandic mathematician and logician working in universal algebra, lattice theory, model theory and set theory. He was emeritus distinguished professor of mathematics at Vanderbilt .... External links ''Algebra Universalis'' on Springer.com''Algebra Universalis'' homepage, including instructions to authors* Universal algebra Mathematics journals Publications established in 1971 Springer Science+Business Media academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clone (algebra)
In universal algebra, a clone is a set ''C'' of finitary operations on a set ''A'' such that *''C'' contains all the projections , defined by , *''C'' is closed under (finitary multiple) composition (or "superposition"): if ''f'', ''g''1, …, ''gm'' are members of ''C'' such that ''f'' is ''m''-ary, and ''gj'' is ''n''-ary for all ''j'', then the ''n''-ary operation is in ''C''. The question whether clones should contain nullary operations or not is not treated uniformly in the literature. The classical approach as evidenced by the standard monographs on clone theory considers clones only containing at least unary operations. However, with only minor modifications (related to the empty invariant relation) most of the usual theory can be lifted to clones allowing nullary operations. The more general concept includes all clones without nullary operations as subclones of the clone of all at least unary operations and is in accordance with the custom to allow nullary terms and nullary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cichoń's Diagram
In set theory, Cichoń's diagram or Cichon's diagram is a table of 10 infinite cardinal numbers related to the set theory of the reals displaying the provable relations between these Cardinal characteristic of the continuum, cardinal characteristics of the continuum. All these cardinals are greater than or equal to \aleph_1, the smallest uncountable cardinal, and they are bounded above by 2^, the cardinality of the continuum. Four cardinals describe properties of the ideal (order theory), ideal of sets of Lebesgue measure, measure zero; four more describe the corresponding properties of the ideal of meagre set, meager sets (first category sets). Definitions Let ''I'' be an ideal (set theory), ideal of a fixed infinite set ''X'', containing all finite subsets of ''X''. We define the following "Cardinal function, cardinal coefficients" of ''I'': *\operatorname(I)=\min\. ::The "additivity" of ''I'' is the smallest number of sets from ''I'' whose union is not in ''I'' any more. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
