Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo – Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann – Bernays – Gödel set theory, a conservative extension of ZFC.

Pfanzagl's axiomatization was endorsed by Oskar Morgenstern: " Von Neumann and I have anticipated " the question whether probabilities " might, perhaps more typically, be subjective and have stated specifically that in the latter case axioms could be found from which could derive the desired numerical utility together with a number for the probabilities ( cf.

Although not formalised and acknowledged as a mythos per se, Lovecraft did correspond with contemporary writers ( Clark Ashton Smith, Robert E. Howard, Robert Bloch, Frank Belknap Long, Henry Kuttner, and Fritz Lieber – a group referred to as the " Lovecraft Circle ") – and shared story elements: Robert E. Howard's character Friedrich Von Junzt reads Lovecraft's Necronomicon in the short story " The Children of the Night " ( 1931 ), and in turn Lovecraft mentions Howard's Unaussprechlichen Kulten in the stories " Out of the Aeons " ( 1935 ) and " The Shadow Out of Time " ( 1936 ).

German Chancellor Wirth arranged for Krupp to secretly continue designing artillery and tanks, coordinating with army chief Von Seeckt and navy chief Paul Behncke.

Von Trier's use of sexually explicit images in The Idiots ( 1998 ) started a wave of arthouse mainstream films with unsimulated sex, such as Catherine Breillat's Romance ( 1999 ), Baise-Moi ( 2000 ), Intimacy ( 2001 ), Vincent Gallo's The Brown Bunny ( 2003 ) and Michael Winterbottom's 9 Songs ( 2004 ).

Von Trier's latest work is Melancholia, a psychological disaster drama ; shot between 22 July and 8 September 2010 at Film i Väst's studios in Trollhättan, Sweden, and with exteriors in the area surrounding the Tjolöholm Castle.

" Doctor Doom, MODOK, and Abomination fall back to Castle Doom only to find that Doctor Doom's mother Cynthia " Coco " Von Doom had converted it into a spa with Chthon's help.

It features interviews with friends, peers, and admirers such as Dave Grohl, Slash, Ozzy Osbourne, James Hetfield, Lars Ulrich, Kirk Hammett, and Robert Trujillo of Metallica, David Ellefson of Megadeth, Scott Ian of Anthrax, Alice Cooper, Peter Hook of Joy Division / New Order, Dee Snider, Nikki Sixx, Mick Jones of The Clash, Kat Von D, Henry Rollins, Lars Frederiksen of Rancid, Jim Heath of Reverend Horton Heat, Slim Jim Phantom of The Stray Cats, Mike Inez, Joan Jett, pro skateboarder Geoff Rowley, pro wrestler Triple H, Fast Eddie Clarke, Jarvis Cocker, Marky Ramone, former Hawkwind

Von Siebold stayed with Döllinger, where he came in regular contact with other scientists.

In September 2011 researchers also proved that a quantum computer can be made with a Von Neumann architecture ( separation of RAM ).

Von Humboldt argued that languages with an inflectional morphological type, such as German, English and the other Indo-European languages were the most perfect languages and that accordingly this explained the dominance of their speakers over the speakers of less perfect languages.

However, a striking example of the line used to divide Dada and Surrealism among art experts is the pairing of 1925's Little Machine Constructed by Minimax Dadamax in Person ( Von minimax dadamax selbst konstruiertes maschinchen ) with The Kiss ( Le Baiser ) from 1927 by Max Ernst.

But San Francisco's defense tightened up on the next 3 plays, forcing 2 incompletions and a completed pass for no gain, and Miami was forced to settle for Von Schamann's second field goal of the game to cut their deficit to 28-13 with 12 seconds left in the half.

A reason Von Braun, head of NASA's Marshall Space Flight Center during the 1960s, advocated for a smaller station after his large one was not built was that he wished to provide his employees with work beyond developing the Saturn rockets, which would be completed relatively early during Project Apollo.

* Moritz Von Oswald-drums ( 1985 onwards ), percussion on " Wild and Lonely ": also composed some songs on Outernational and did various remixes of Associates songs with Ralf Hertwig.

Von Laue worked with two technicians, Walter Friedrich and his assistant Paul Knipping, to shine a beam of X-rays through a copper sulfate crystal and record its diffraction on a photographic plate.

Moltke had indeed massed three armies in the area — the Prussian First Army with 50, 000 men, commanded by General Karl Von Steinmetz opposite Saarlouis, the Prussian Second Army with 134, 000 men commanded by Prince Friedrich Karl opposite the line Forbach – Spicheren, and the Prussian Third Army with 120, 000 men commanded by Crown Prince Friedrich Wilhelm, poised to cross the border at Wissembourg.

The contemporary historians Sozomen and Theodoret were combined with Socrates in a sixth-century compilation, which has obscured their differences until recently, when their individual portrayals of the series of Christian emperors were distinguished one from another and contrasted by Hartmut Leppin, Von Constantin dem Großen zu Theodosius II ( Göttingen 1996 ).

* Von der Heydt Museum is an important art gallery with works by 19th-and 20th-century artists.

Von Kulmbach then apprenticed with Albrecht Dürer and after Dürer retired from painting altarpieces in 1510 Kulmbach took over most of his commissions.

However, the subsequent period saw the departure of manager van Gaal along with an exodus of many key players including Clarence Seedorf in 1995 ; Edgar Davids, Michael Reiziger, Finidi George, and Nwankwo Kanu in 1996 ; Patrick Kluivert, Marc Overmars, and Winston Bogarde in 1997 ; Ronald de Boer and Frank de Boer in 1998 ; and Edwin van der Sar and Jari Litmanen in 1999.

In 1995, the year Ajax won the Champions League, the Dutch national team was almost entirely composed of Ajax players, with Edwin van der Sar in goal ; players such as Michael Reiziger, Frank de Boer, and Danny Blind in defense ; Ronald de Boer, Edgar Davids, and Clarence Seedorf in midfield ; and Patrick Kluivert and Marc Overmars in attack.

* Nederlands Kamerkoor, with Harry van der Kamp, conductor.

Dürer's work on geometry is called the Four Books on Measurement ( Underweysung der Messung mit dem Zirckel und Richtscheyt or Instructions for Measuring with Compass and Ruler ).

His brother-in-law Balthasar van der Ast also lived and worked in his workshop and moved with him on his travels.

Fruit still life with shells painted by Balthasar van der Ast. His sons and his pupil and brother-in-law, Balthasar van der Ast, were among those to uphold the Bosschaert dynasty which continued until the mid-17th century.

The King kept his exclusive sovereignty but was bound by the Government Business to cooperate with the Ministers and the decisions of both Chambers of the States ( de: Kammern der Ständeversammlung ) meeting.

Kamerlingh Onnes and Johannes van der Waals with the helium " liquefactor " in Leiden ( 1908 )

After touring for Celebrity Skin finished, Auf der Maur left the band to tour with The Smashing Pumpkins ; Hole's touring drummer Samantha Maloney left soon after.

Daniel Kehlmann's 2005 novel Die Vermessung der Welt, translated into English as Measuring the World ( 2006 ), explores Gauss's life and work through a lens of historical fiction, contrasting them with those of the German explorer Alexander von Humboldt.

She then studied for two years with the painter Francis Adolf Van der Wielen, who offered lessons in perspective and drawing from casts during the time that the new Pennsylvania Academy of the Fine Arts was under construction.

In 1584, the pastor and chronicler Balthasar Russow in his Chronica der Provinz Lyfflandt ( 1584 ) wrote of an established tradition of setting up a decorated spruce at the market square where the young men " went with a flock of maidens and women, first sang and danced there and then set the tree aflame ".

Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen (" On the invariant properties of special binary forms, in particular the spherical harmonic functions ").

One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in mathematical logic, and co-authored with him the important book Grundlagen der Mathematik ( which eventually appeared in two volumes, in 1934 and 1939 ).

A clear exposition of the " errors " of Euclid and of the solutions presented in the Grundlagen der Geometrie, with reference to non-Euclidean geometry.

On November 18, von Hindenburg testified in front of this parliamentary commission, and cited a December 17, 1918 Neue Zürcher Zeitung article that summarized two earlier articles in the Daily Mail by British General Frederick Barton Maurice with the phrase that the German army had been ' dagger-stabbed from behind by the civilian populace ' (" von der Zivilbevölkerung von hinten erdolcht .").

* 1808 – Ludwig van Beethoven conducts and performs in concert at the Theater an der Wien, Vienna, with the premiere of his Fifth Symphony, Sixth Symphony, Fourth Piano Concerto ( performed by Beethoven himself ) and Choral Fantasy ( with Beethoven at the piano ).

While superior to the van der Waals equation of state, it performs poorly with respect to the liquid phase and thus cannot be used for accurately calculating vapor-liquid equilibria.

Then he announced to the world: " The independence of Austria, for which he has fallen, is a principle that has been defended and will be defended by Italy even more strenuously ", and then replaced in the main square of Bolzano the statue of Walther von der Vogelweide, a Germanic troubadour, with that of Drusus, a Roman general who conquered part of Germany.

At the start of 1986, Essendon were considered unbackable for three successive flags, but a succession of injuries to key players Paul Van der Haar ( only fifteen games from 1986 to 1988 ), Tim Watson, Darren Williams, Roger Merrett and Simon Madden led the club to win only eight of its last eighteen games in 1986 and only nine games ( plus a draw with Geelong ) in 1987.

Bulwer-Lytton is also credited with the appellation for the Germans " Das Volk der Dichter und Denker ", that is, the people of poets and thinkers.

* Correspondence with Frederick the Great at Digitale Ausgabe der Universitätsbibliothek Trier