41. Skolem Arrays skolem arrays are an extension of skolem sequences which were studied inthe 1950s by the Norwegian mathematician thoralf skolem(18871963). http://mathcs.mta.ca/research/cbaker/skolem/

Skolem Arrays Last updated July 7th, 1999 Skolem arrays are a combinatorial construct developed by Dr. C. Baker, Dr. A. Bonato and Patrick Kergin for a summer NSERC grant at Mount Allison University in Sackville New Brunswick. Skolem arrays are an extension of Skolem sequences which were studied in the 1950s by the Norwegian mathematician Thoralf Skolem(1887-1963). A Skolem sequence of order n is a sequence of integers which satisfies the following properties: The two occurrences of i are exactly i integers apart. The sequence is an example of a Skolem array of order 8. I Making a Skolem Array II Our results III C++ Programs IV Acknowledgements Patrick Kergin Mount Allison University Sackville New Brunswick pekrgn@mta.ca

42. The Results Of Our Project The Results of Our Project. thoralf skolem proved that n = 0,1 mod 4 was anecessary and sufficient condition for the existence of skolem sequences. http://mathcs.mta.ca/research/cbaker/skolem/results.htm

The Results of Our Project Thoralf Skolem proved that n 0,1 mod 4 was a necessary and sufficient condition for the existence of Skolem sequences. Similarly, we have proven that n 0,1 mod 4 is also a necessary and sufficient condition for the existence of Skolem arrays. Despite this, we have yet to find a direct link between Skolem sequences and Skolem arrays. We have also worked with the enumeration of Skolem arrays. Using extensions (a process by which we can create arrays of a certain order using two arrays of lesser order), we have provided an exponential lower bound on the number of Skolem arrays. Current research is devoted to finding a link between Skolem arrays and combinatorial designs. A split pair occurs when the two instances of a number appear on different rows. We conjecture that in all Skolem arrays, the number of split pairs is greater than or equal to the number of unsplit pairs. A paper based on our findings has been submitted to "Ars Combinatoria" for eventual publication. Back to Main

43. Who Are Boole, Fitch, And Tarski? skolem, thoralf (18871963) Norwegian logician known especially for the Löwenheim-skolem Theorem and skolem s Paradox It follows from the Löwenheim-skolem http://www.ucalgary.ca/~rzach/279/logicians.html

Who are Boole, Fitch, and Tarski? Here's a list of the logicians that show up in Barwise and Etchemendy's Language, Proof, and Logic and in the exercise files for Tarski's World. Most names are linked to websites with more information. Abelard, Peter French theologian and philosopher best known for his work on the problem of universals. He is also known for his poetry and for his celebrated love affair with Heloise Abelard and Heloise were the original celebrity couple. Ackermann, Wilhelm German logician and student of Hilbert . Gave the first direct consistency proof of a non-trivial mathematical theory, and contributed to research on the decision problem. Co-author (with Hilbert) of Aristotle (384-322 BCE) Ancient Greek philosopher and founder of logic as an independent discipline. His theory of categories and syllogisms as presented in On Interpretation and the Prior Analytics shaped the field of logic up until the 19th century. Arnauld, Antoine

44. Bibliography Kazan. Univ. 1966. skolem, thoralf Albert, 18871963, Selected works in logic,by Th. skolem / edited by Jens Erik Fenstad, Oslo, Universitetsforlaget, 1970. http://www.library.cornell.edu/math/bibliography/display.cgi?start=S&

45. Forskning.no: Matematisk Vekst I Abels Fotspor Også Axel Thue, thoralf skolem, Viggo Brun, Ernst Selmer, Vilhelm thoralfskolem publiserte hele 177 avhandlinger i løpet av sin lange karriere. http://www.forskning.no/Artikler/2002/juni/1023116423.71

gå til forsiden spør en forsker abonner på nyhetsbrev kontakt oss ... Naturvitenskap i fokus Forskningsåret 2003 Det er ikke sunt å pynte seg - og annen god lærdom fra biologien Det meste av det menneskelige er oss fremmed Frankenfood, nazister og knokler på vidvanke ... Væråret 2003 - mot normalt? forskning.no Sagveien 23b Pb. 2070 Grünerløkka 0505 OSLO tel 22 80 98 90 fax 22 80 98 99 epost@forskning.no Ansvarlig redaktør: Steinar Q. Andersen Faglig redaktør: Erik Tunstad © forskning.no 2004 Medeiere i forskning.no: Agderforskning Høgskolen i Bergen Høgskolen i Bodø Høgskolen i Oslo ... Universitetet i Tromsø Forskning.no har mottatt Merket for God Design i samarbeid med Creuna AS. denne tjenesten er designet og utviklet av Matematisk vekst i Abels fotspor 04.Jun 2002 07:00 Av: Bjarne Røsjø , Informasjonsrådgiver Niels Henrik Abel er ett av de største matematiske genier verden har fostret, og årets 200-årsjubileum brukes til å markere hans innsats. Det er ikke fullt så godt kjent at det grodde friskt i sporene etter Abel så godt at Norge nærmest var en matematisk stormakt på slutten av 1800-tallet og langt utover på 1900-tallet. - Du skal ikke åpne mange lærebøker i avansert matematikk før du støter på Axel Thues teorem, Sophus Lies grupper eller Ludwig Sylows teorier. Norge som nasjon var overrepresentert med fremragende matematikere på slutten av 1800-tallet, forteller Geir Ellingsrud, som er professor i matematikk ved UiO og deltaker i årets forskningsgruppe i matematikk ved SHS.

46. Open Directory - Science: Math: Logic And Foundations: History: People: Skolem, Mints, Matti Eklund on skolem s life and work. thoralf skolem (18871963)- Biography from MacTutor History of mathematics archive. http://www.newhoo.com/Science/Math/Logic_and_Foundations/History/People/Skolem,_

about dmoz add URL update URL become an editor ... help the entire directory only in People/Skolem,_Thoralf Top Science Math Logic and Foundations ... People : Skolem, Thoralf Skolem Issue of the Nordic Journal of Philosophical Logic - Special issue with articles by Jens Erik Fenstad, Herman Ruge Jervell, Hao Wang, Grigori Mints, Matti Eklund on Skolem's life and work. Thoralf Skolem (1887-1963) - Biography from MacTutor History of mathematics archive. Skolem, Thoralf " search on: All the Web AltaVista Google USENET Google ... Yahoo This category needs an editor Last update: 16:01 PT, Thursday, March 30, 2000 - edit

47. Descendants Of Morten Anundsøn Strenge skolem, Svein (1879 ) C. skolem, thoralf Albert (1871-1886) C. skolem,thoralf Albert (1887- ) C. skolem, Thorbjørn Tøgersen (1889-1940) P,P. http://home.no.net/arnehol/genealogy/Lintvedt/Names33.htm

My Lintvedt family, descendants of Morten Anundsøn Strenge A B C D ... P , Q, R S T U ... W , X, Y, Z About this family Names Saatvedt, Anna (1929- ) C Saatvedt, Astrid (1920- ) C Saatvedt, Berit (1959- ) C Saatvedt, Gjertrud Irene (1934- ) P Saatvedt, Haldis Kristine Grosvold (1923- ) P Saatvedt, Ingrid (1927- ) C Saatvedt, Ivar Ole ( - ) S Saatvedt, Kjell (1963- ) C Saatvedt, Knut Wilhelm Omholt (2001- ) C Saatvedt, Kristian Olausen (1926- ) C Saatvedt, Magne Vincent (1934- ) C Saatvedt, Olav (1932-1935) C Saatvedt, Ole Kristian (1997- ) C Saatvedt, Ole Lukassøn (1764-1848) S Sabel, Ingrid Marie ( - ) C Sabel, James Robert (1956- ) C Sabel, John Gordon ( - ) C Sabel, Karen Louise ( - ) C Sabel, Kristin Elaine (1962- ) C Sabel, Paul Frederick ( - ) C Sabel, Robert Walter ( - ) S Sæther, Arne ( - ) S Sæthre, Anne ( -1949) S Sæthre, Signy ( - ) P Sætra, Anne Grethe (1965- ) S Sætra, Asbjørn Ludvig (1938- ) P Sætra, Erik Torbjørn (1943- )

48. My Johnson Family, Descendants Of Morten Anundsøn Strenge 2286 M i. thoralf Albert skolem was born on 15 May 1871 and died on 6 Jan 1886, atage 14. 2287 M ii. 2291 M vi. thoralf Albert skolem was born on 23 May 1887. http://home.no.net/arnehol/genealogy/Lintvedt/D9.htm

My Johnson family, descendants of Morten Anundsøn Strenge Ninth Generation 1205. Hanna Sofie Aannestad Berte Marie Andersdatter Røsholt , Anders Pålsøn Røsholt , Berte Marie Hansdatter Hvål , Sigrid Anundsdatter Søum , Anund Mortensøn , Morten Anundsøn , Anund Mortensøn , Morten Anundsøn ) was born in 1852 in Grette, Sandsvær, Bu. and died in 1886, at age 34. Hanna married Anton Nikolai Hanssen Tofstad in 1875. Anton was born in 1854 and died in 1911, at age 57. Children from this marriage were: 2209 M i. Hans Tofstad was born in 1875 and died in 1878, at age 3. + 2210 F ii. Betsy Jørgine Tofstad was born on 10 Jan 1882 in Sandsvær, Bu. and died in 1964, at age 82. 2211 M iii. Halvor Tofstad was born in 1877 and died in 1901, at age 24. He never married. 2212 M iv. Hans Tofstad was born in 1879 and died in 1906, at age 27. He never married. 2213 F v. Gunda Marie Tofstad was born in 1884 and died in 1907, at age 23. 1208. Helle Syrene Paulsdatter Røsholt Paul Andersøn Røsholt , Anders Pålsøn Røsholt , Berte Marie Hansdatter Hvål , Sigrid Anundsdatter Søum , Anund Mortensøn , Morten Anundsøn , Anund Mortensøn , Morten Anundsøn ) was born in 1843 in Røsholt, Sandsvær, Bu. and died in 1879, at age 36.

49. The Mathematics Genealogy Project - Index Of SK Skokan, Jozef, Emory University, 2000. skolem, thoralf, Universiteteti Oslo, 1926. Skoogh, Daniel, Chalmers University of Technology, 1998. http://genealogy.impa.br/html/letter.phtml?letter=SK

50. Wiki: SkolemFunction finite model. In 1922, thoralf skolem presented a complete proof ofthis theorem (which is now called the Löwenheimskolem Theorem). http://gnufans.net/intrspctr.pl?SkolemFunction

51. Model Theory. Goedel's Completeness Theorem. Skolem's Paradox. Ramsey's Theorem. Initially, Model Existence theorem was proved in a weaker form in 1915 (by LeopoldLoewenheim) and 1919 (by thoralf skolem) if a first order theory has a model http://www.ltn.lv/~podnieks/gta.html

model theory, Skolem paradox, Ramsey theorem, Loewenheim, categorical, Ramsey, Skolem, Gödel, completeness theorem, categoricity, Goedel, theorem, completeness, Godel Back to title page Left Adjust your browser window Right Appendix 1. About Model Theory Some widespread Platonist superstitions were derived from other important results of mathematical logic (omitted in the main text of this book): Goedel's completeness theorem for predicate calculus, Loewenheim-Skolem theorem, the categoricity theorem of second order Peano axioms. In this short Appendix I will discuss these results and their methodological consequences (or lack of them). All these results have been obtained by means of the so-called model theory . This is a very specific approach to investigation of formal theories as mathematical objects. Model theory is using the full power of set theory. Its results and proofs can be formalized in the set theory ZFC Model theory is investigation of formal theories in the metatheory ZFC. The main structures of model theory are interpretations . Let L be the language of some (first order) formal theory containing constant letters c , ..., c

52. Resolution Method. Normal Forms. Skolem. Mathematical Logic. Part 5. The second step (idea 2b, due to thoralf skolem) allows elimination of existentialquantifiers. It was first introduced by thoralf skolem (18871963) in 1928 http://www.ltn.lv/~podnieks/mlog/ml5.htm

normal form, prenex, disjunctive, conjunctive, form, normal, DNF, CNF, prenex normal form, Skolem normal form, disjunctive normal form, conjunctive normal form, Skolem Back to title page Left Adjust your browser window Right 5. Normal Forms. Resolution Method Prenex normal form Conjunctive and disjunctive normal forms Skolem normal form Clause form ... Resolution method for predicate formulas In this section, we will try to produce a practical method allowing to prove theorems by using computers. In general, this task is not feasible because of its enormous computational complexity (see Section 6 ). Still, for problems of a "practical size" (arising, for example, in deductive databases and other artificial intelligence systems, or, trying to formalize real mathematical proofs), such methods are possible and some of them are already successfully implemented. Mizar project QED project Classical logic only... Main Ideas If F , ..., F n is the set of our assumptions (facts, rules, axioms, hypotheses etc.), does the assertion G follow from this set? One of the well known approaches to proving theorems in mathematics are the so-called refutation proofs (reductio ad absurdum) - proofs by deriving a contradiction: assume ~G, and derive a contradiction. I.e. prove that F

53. SearchBug Directory: Science: Math: Logic_and_Foundations: History: People Jan (7) Peirce, Charles Sanders (11) Post, Emil L. (6) Prior, Arthur Norman (2),Quine, Willard van Orman (12) Russell, Bertrand (23) skolem, thoralf (2) Tarski http://www.searchbug.com/directory.aspx/Science/Math/Logic_and_Foundations/Histo

All Searches Auctions CompanyFinder Entertainment ... Travel Search the Web: Web Images Audio Files News Multimedia Shopping Open Directory Search: Featured Websites Ancestry.com - Free Trial - click.atdmt.com Genealogy database covers 1.2 billion documents and 1 billion names. Find everything you need to research your family. Yahoo! Personals - Where Singles Meet - personals.yahoo.com Make the first move! Search photo ads and create your own profile - both FREE. Click Now! Now You Can Find Anyone In the US! - find.intelius.com People Search helps you locate family and old friends or anyone fast! We search billions of records that give you instant answers on how to quickly make contact today. Click here now to start your search and order! Find Romance With Other Catholic Singles - catholicpeople.com Find Local and Out of Town Romance with other Catholic Singles. Find the Catholic men and women you really want to meet! Safe, discreet, and confidential. Click now to sign up for free and to meet new people, become friends, or find true love! People Science Math Logic and Foundations History ... Go to Directory Home Categories Aristotle Bernays, Paul

54. The Norwegian Mathematical Society. Matematisk Tidsskrift ( The Norwegian Mathematical Journal ) appeared in 1919,opening, sadly, with the obituary of Ludvig Sylow, written by thoralf skolem. http://www.matematikkforeningen.no/enghist.html

The Norwegian Mathematical Society Some history by Bent Birkeland [The summary of the society's history below is not a direct translation of the Norwegian page Historikk (also by Bent Birkeland).] The first attempt to create a mathematical society in Norway was made in 1885 by Sophus Lie, who was at that time professor in Oslo. This was a time when similar initiatives took place in many European countries. Moscow Mathematical Society was founded in 1864, London in 1865, the Finnish, French and Danish ones in 1868, -72 and -73, respectively. In Norway, however, the mathematical community at that time was too small, and the venture broke down when Lie moved to Leipzig the following year. But a series of reforms in the high schools and at the university (less Latin and Greek, more modern languages, science and mathematics) during the second half of the 1800's led to a marked expansion of that community, and a formal organisation became necessary. In particular the need for a Norwegian mathematical journal was felt. The difficulty was of course to find financial support for it, and to find persons able and willing to take on the editorial work. In 1918 the time had come. Preliminary discussions took place in the early autumn. Arnfinn Palmstrøm, who at that time worked as an actuary, and from 1919 until his

55. Kurze Charakteristik Des Faches Translate this page von Gödel für die Arithmetik und die Logik höherer Stufe, der Nachweis der Nichtcharakterisierbarkeitder natürlichen Zahlen durch thoralf skolem und die http://www-computerlabor.math.uni-kiel.de/~spinas/Logik.htm

Mathematisches Seminar Zur Geschichte der Logik Aristoteles George Boole und Gottlob Frege Die Abwehr der Antinomien, die um die Wende zum zwanzigsten Jahrhundert entdeckt wurden, war das zentrale Thema der Logik zu Beginn des zwanzigsten Jahrhunderts. Bertrand Russell Georg Cantor geschaffene Mengenlehre wurde durch die Axiomatik von Ernst Zermelo und Abraham (Adolf) Fraenkel konsolidiert. Luitzen E. Brouwer vertrat eine radikale konstruktivistische Position, nach der auf wesentliche Teile der klassischen Mathematik zu verzichten sei. Um deren Bestand durch formale Widerspruchsfreiheitsbeweise zu retten, entwickelte David Hilbert als Gegenposition das Programm der Beweistheorie. bewies und Anatolij Malcev Thoralf Skolem Alonzo Church und Alan Turing prinzipielle Grenzen aller formalen Methoden auf. Alfred Tarski beteiligt war. Heute ist die Modelltheorie eng mit klassischen mathematischen Disziplinen verwoben. Exemplarisch seien die von Abraham Robinson Thoralf Skolem John von Neumann Paul Bernays und Paul Cohen Gerhard Gentzen Alonzo Church und Alan Turing die von Stephen Kleene und Emil Post stehen.

56. Beezer's Academic Genealogy Albert thoralf skolem TCSGMHMBDM; Axel Thue TCSGMHM BDM;Marius Sophus Lie MHM; Peter Ludwig Mejdell Sylow MHM. The http://buzzard.ups.edu/genealogy.html

Beezer's Academic Genealogy Here it is the succession of PhD advisers and students that goes backwards in time from my own degree. For the later entries it is not clear that there was a formal advisor/student/degree relationship, but there is evidence that one person was influenced in their education by the other. It seems odd that [TCSG] lists Ore as a student of Skolem, with Ore's degree awarded in 1924 while [BDM] lists Skolem's degree as being given in 1926. Tree Paul Morris Weichsel (Cal Tech 1960) [ MGP Richard Albert Dean (Ohio State 1953) [ MGP Marshall Hall, Jr. (Yale University 1936) [ MGP TCSG MGP TCSG Albert Thoralf Skolem [ TCSG MHM ][BDM] Axel Thue [ TCSG MHM ] [BDM] Marius Sophus Lie [ MHM Peter Ludwig Mejdell Sylow [ MHM The following quotes are from articles in the Biographical Dictionary of Mathematicians [BDM]: Skolem: "In the latter year [1916] he returned to Oslo, where he was made Dozent in 1918. He received his doctorate in 1926." (H. Oettel, p. 2296) Thue: "Thue enrolled at Oslo University in 1883 and became a candidate for the doctorate in 1889." (Viggo Brun, p. 2460)

57. Norsk Matematisk Forening De som kom til å sitte lengst, var Olaf Thalberg som var med i redaksjonenfra 1921 til 1945, og thoralf skolem, med et opplag på 5600. http://www.geocities.com/CapeCanaveral/Hangar/3736/nmf.htm

Norsk Matematisk Forening Norsk Matematisk Forening ble stiftet den 2. november 1918, og det kan være av interesse å se litt på det foreningens protokoller forteller om dens første tid. Det stifterne så som foreningens viktigste oppgave, var å holde god kontakt mellom de ulike matematiske miljøene i landet. Foruten universitet og skole var det særlig det forsikringstekniske miljøet og geodetene i Norges Geografiske Oppmåling som var interesserte. Man sørget da også for at det til enhver tid, i alle dall til uti 1940-årene, var personer fra alle disse miljøene i foreningens styre. La oss begynne med et par ord om hovedpersonene bak stiftelsen. Poul Heegaard (1871-1948) var dansk, hadde vært professor i København fra 1910, og var nettopp i 1918 utnevnt i et nyopprettet professorat i geometri i Oslo (byen het den gang Kristiania). I geometrien er han særlig kjent for sin doktoravhandling fra 1899, der han rydder opp i noen topologiske uklarheter i Poincarés arbeider. Heegaard-invarianter er fortsatt et nyttig begrep i topologien. Han var sterkt interessert i undervisnings- og opplysningsvirksomhet, og nedla et stort arbeid på dette området. Arnfinn Palmstrøm (1867-1922), var aktuar, og ble i 1919 professor i forsikringsmatematikk. Det var han og Heegaard som sammen gjorde det meste av forarbeidet til foreningens stiftelse. De forfattet en henvendelse til “matematikk-interesserte personer landet over” om planene for en matematisk forening, de skrev utkast til vedtekter for foreningen, og de søkte økonomisk støtte fra staten, og fra livsforsikringsselskapene.

58. Axiom Schema Of Replacement The axiom was independently discovered by thoralf skolem later in the same year,and it is in fact skolem s final version of the axiom list that we use today http://www.fact-index.com/a/ax/axiom_schema_of_replacement.html

Main Page See live article Alphabetical index Axiom schema of replacement In axiomatic set theory and the branches of logic mathematics , and computer science that use it, the axiom schema of replacement is a schema of axioms in Zermelo-Fraenkel set theory Suppose P is any predicate in two variables that doesn't use the symbol B . Then in the formal language of the Zermelo-Fraenkel axioms, the axiom schema reads: X Y P X Y A B C C B D D A P D C or in words: If given any set X , there is a unique set Y such that P holds for X and Y , then, given any set A there is a set B such that, given any set C C is a member of B if and only if there is a set D such that D is a member of A and P holds for D and C Note that there is one axiom for every such predicate P ; thus, this is an axiom schema. To understand this axiom, first note that the clause in the first set of parentheses above is exactly what one needs to construct a functional predicate F in one variable such that F X Y if and only if P X Y ). Indeed, if one formalises the language of predicate logic to allow the use of derived functional predicates in axiom schemas, then the axiom schema may be rewritten as: A B C C B D D A C F D for each derived functional predicate F in one variable; or in words:

59. Best Viewed In 24pt And Full-screen Translate this page skolem, Albert thoralf (Norvège, 1887-1963). skolem établit la versiondéfinitive du théorème de Löwenheim-skolem tout ensemble http://www.irisa.fr/lande/ridoux/LPAZ/node62.html

Best viewed in 24pt and full-screen Next: T Up: A-Z Previous: R S dynamic s . Scission d'une liste de longueur paire en deux moitiés. S rel. logique combinatoire ) Combinateur de la logique combinatoire régi par l'axiome suivant. Il est définissable en -calcul et en Prolog : comb_S S :- pi x (pi y (pi z ( (S x y z) = (x z (y z)) ))) . Semi-décidable adj. rel. décidable ) Se dit d'un problème de décision pour lequel il n'existe au mieux que des procédures qui terminent toujours dans les cas de succès et peuvent ne pas terminer dans les cas d'échec. On appelle ces procédures des semi-algorithmes Séquent n. m. rel. calcul des séquents ) Assemblage de formules qui énonce que la disjonction des est une conséquence de la conjonction des . Un cas particulier intéressant est celui des séquents intuitionnistes. Ce sont les séquents où Un autre cas particulier est celui des séquents de type. Un séquent de type énonce que a le type dans le contexte . La forme exacte du contexte dépend du système de type et de sa présentation, mais il s'agit généralement d'une collection d'assertion de typage, . Par exemple, dans le cas des

60. Biography-center - Letter S Skoblikova, Lidiya www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=71478;skolem, thoralf wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/skolem http://www.biography-center.com/s.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish S 993 biographies Sa, Zitkala www.ipl.org/div/natam/bin/browse.pl/A91 Sa, Zitkala voices.cla.umn.edu/authors/GertrudeSimmonsBonnin.html Saarikoski, Pentti www.kirjasto.sci.fi/psaariko.htm Sabatier, Paul www.nobel.se/chemistry/laureates/1912/sabatier-bio.html Sabin, Florence library.thinkquest.org/20117/sabin.html Saccheri, Giovanni www-history.mcs.st-and.ac.uk/~history/Mathematicians/Saccheri.html Sacchi, Andrea www.kfki.hu/~arthp/bio/s/sacchi/biograph.html Sacchi, Andrea www.getty.edu/art/collections/bio/a3459-1.html Sachs, Bernard www.whonamedit.com/doctor.cfm/403.html Sachs, Hans www.whonamedit.com/doctor.cfm/1835.html Sachs, Hans www.theatrehistory.com/german/sachs001.html Sachs, Nelly www.nobel.se/literature/laureates/1966/sachs-autobio.html Sacks, Oliver

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