In class theories such as Von Neumann – Bernays – Gödel set theory and Morse – Kelley set theory, there is a possible axiom called the axiom of global choice which is stronger than the axiom of choice for sets because it also applies to proper classes.

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.

Von Neumann wrote the first array-sorting program ( merge sort ) in 1945, during the building of the first stored-program computer .< sup > p.

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.

The modern computer, or Von Neumann machine, would play a central role in cognitive science, both as a metaphor for the mind, and as a tool for investigation.

Some argue that the concept of the collapse of a " real " wave function was introduced by Heisenberg and later developed by John Von Neumann in 1932.

Von Neumann himself used the term Universal Constructor.

As a serious proposal, it was first suggested by mathematician John Von Neumann in the late 1940s when he proposed a kinematic self-reproducing automaton model as a thought experiment.

See Von Neumann, J., 1966, The Theory of Self-reproducing Automata, A. Burks, ed., Univ.

The design could be modified to build Von Neumann probes to explore the galaxy.

The movie Screamers, based on Dick's short story Second Variety, features a group of robot weapons created by mankind to act as Von Neumann devices / berserkers.

In 1968, just before he published the first volume, Knuth accepted a job working on problems for the National Security Agency ( NSA ) through their FFRDC the Institute for Defense Analyses ( IDA ) Communications Research Division situated at the time on the Princeton campus in the Von Neumann building as stated in his cumulae vitae.

In work on Zermelo – Fraenkel set theory, the notion of class is informal, whereas other set theories, such as Von Neumann – Bernays – Gödel set theory, axiomatize the notion of " class ", e. g., as entities that are not members of another entity.

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

* Von Neumann machine

* Mathematics: Von Neumann universe

As far as computer security is concerned, reasoning about the security properties of a computer system requires being able to make sound assumptions about what it can, and more importantly, cannot do ; however, barring any reason to believe otherwise, a computer is able to do everything that a general Von Neumann machine can.

Von Neumann machine may refer to:.

* Von Neumann architecture, a conceptual model of a computer architecture

** Von Neumann probes, hypothetical space probes capable of self-replication

Von Neumann used 10 digit numbers, but the process was the same.

Von Neumann was aware of this, but he found the approach sufficient for his purposes, and was worried that mathematical " fixes " would simply hide errors rather than remove them.

Von Neumann judged hardware random number generators unsuitable, for, if they did not record the output generated, they could not later be tested for errors.

Both Von Neumann as well as various degrees of Harvard architectures are used.

The monoliths are clearly described in the novels as being controlled by internal computer, just like Von Neumann machines.

The history of agent-based modeling can be traced back to Von Neumann machines, the concept of a machine capable of reproduction.

Von Neumann himself used the term universal constructor to describe such self-replicating machines.

* Baron Von Skull and Tor — Baron Von Skull is an elderly World War One flying ace from Germany, who creates evil war machines.

The first group consisted of Alan Turing, Alonzo Church and Otto Von Newman, who were working to develop computing machines and the mathematical underpinnings of computer science.

Inevitables are built and programmed in automated factories called creche-forges ; one of them, mentioned in the Manual of the Planes, is called Neumannus ( a reference to Von Neumann machines ).

Von Platen himself did not live to see the completion of the canal, having died shortly before its opening.

As with the Von der Tann design, which was drawn up at a similar time, all guns could be fired either side in broadsides, meaning more guns could come to bear than with the Helgoland design, despite having fewer in total.

Von Mises never totally formalized his definition of a proper selection rule for sub-sequences, but in 1940 Alonzo Church defined it as any recursive function which having read the first N elements of the sequence decides if it wants to select element number N + 1.

Von Rundstedt and Model deemed a big Allied offensive to be imminent, having received many intelligence reports that described a ' constant stream ' of reinforcements to the right wing of the British Second Army.

Von Galen, the English subsidies having remained largely hypothetical, made peace with the Republic in April at Cleves.

Mannerheim was also of Scottish ancestry on his paternal side, his ancestor George Wright ( the founder of the Von Wright line of Finnish nobility ) having emigrated from Dundee to Sweden in the 17th century.

Von Spee, having learned of the presence of Glasgow off Coronel, sailed south from Valparaíso with all five warships with the intention of destroying her.

In April, World Class suffered another death when Mike Von Erich-who now was diagnosed with toxic shock syndrome-was found dead near Lake Lewisville, having committed suicide by overdosing on Placidyl.

The series ended with the ED and MRU teams having a dinner to farewell the last remaining original character, Von Ryan ( Judith McGrath ), on her final day at All Saints.

Von Bock is released when the next Czar ascends the throne, but by that time he is having mental problems during his last years under house arrest.

Von Richthofen was suffering from headaches and exhaustion and was diagnosed as having a brain tumor.

Von Bülow graduated from Trinity College, Cambridge, and worked as personal assistant to J. Paul Getty after having practised law in London in the 1950s.

In the temple, Jones faces Von Beck, who pursues him in a tank, bent on having revenge for the crocodile attack.

Von Wrangel was the first of a series of bachelor appointees to the office of governor who had to find a wife before assuming the duties in America, the Russian American Company rules having been changed in 1829.

Von Knyphausen returned to Europe, having, as he said, achieved neither glory nor advancement.

Von Bork and his diplomat friend Baron von Herling disparage their British hosts, having judged them rather negatively.

Chris though was involved in two angles years before: one involving Chris smashing Buddy Roberts across the back with a chair, and another well-known incident involved Chris tackling Gino Hernandez at the Cotton Bowl in 1985 ; while escaping from having his hair shaved off following a tag-team loss at the hands of the Von Erichs.

Following a WrestleMania VII loss to Kerry Von Erich, he disappeared from WWF TV for several months before having a short run on several Canadian house shows as a babyface in matches against The Mountie.

Being a descendant of Sophia of Hanover, and having rights under the Act of Settlement 1701, as amended by the Sophia Naturalization Act 1705, Prince Frederick was naturalised as a British citizen in October 1947 under the name Mr. Friedrich Von Preussen.

* The class V, the universal class having all possible sets as members, is defined by V is also the Von Neumann universe.