Q:Information: - In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states: The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23problems presented in 1900. he answer to this problem is independent of ZFC set theory (that is, ZermeloFraenkel set theory with the axiom of choice included), so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Godel in 1940. - Wittenberg, officially Lutherstadt Wittenberg, is a town in Saxony-Anhalt, Germany. Situated on the river Elbe, it has a population of about 50,000. - Coswig is a town in the district of Wittenberg of Saxony-Anhalt, Germany. It is situated on the right bank of the Elbe, approx. 12km west of Wittenberg, and 15km east of Dessau. - In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "the Cartesian product of a collection of non-empty sets is non-empty". It states that for every indexed family formula_1 of nonempty sets there exists an indexed family formula_2 of elements such that formula_3 for every formula_4. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. - Friedrich Paul Mahlo ( born July 28 , 1883 in Coswig , Anhalt , died August 20 , 1971 in Halle , Saxony - Anhalt ) was a German mathematician . Mahlo introduced Mahlo cardinals in 1911 . He also showed that the continuum hypothesis implies the existence of a Luzin set . - Georg Ferdinand Ludwig Philipp Cantor ( January 6, 1918) was a German mathematician. He invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware. - In mathematics, ZermeloFraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox. ZermeloFraenkel set theory with the historically controversial axiom of choice included is commonly abbreviated ZFC, where C stands for choice. Many authors use ZF to refer to the axioms of ZermeloFraenkel set theory with the axiom of choice excluded. Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. - Kurt Friedrich Godel (April 28, 1906 January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Godel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. What is the relationship between 'paul mahlo' and 'set theory'?
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field of work