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.

) If formulated in von Neumann – Bernays – Gödel set theory, the surreal numbers are the largest possible ordered field ; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals ; it has also been shown that the maximal class hyperreal field is isomorphic to the maximal class surreal field.

Bernays also drew on the ideas of the French writer Gustave LeBon, the originator of crowd psychology, and of Wilfred Trotter, who promoted similar ideas in the anglophone world in his book Instincts of the Herd in Peace and War.

His father, Isaac Bernays ( 1792-1849 ) was a man of wide culture and the first orthodox German rabbi to preach in the vernacular ; his brother, Michael Bernays, was also a distinguished scholar.

In a series of articles published 1937-54, Paul Bernays modified Von Neumann's theory so as to make sets and set membership primitive ; he also discovered that it could be finitely axiomatized.

* Journalists, writers, publishers: Mathilde Franziska Anneke ; Gustav Bloede ( see Marie Bloede ); Rudolf Doehn ; Carl Adolph Douai ; Carl Daenzer ; Bernard Domschke ; Christian Esselen ( editor of Atlantis ); Julius Fröbel ; Karl Peter Heinzen ; Rudolf Lexow ( founder of Belletristisches Journal ); Niclas Müller ; Reinhold Solger ; Emil Praetorius ; Oswald Ottendorfer ; Friedrich Hassaurek ; Theodor Olshausen ; Hermann Raster ; Wilhelm Rapp ; Carl Heinrich Schnauffer ; Kaspar Beetz ; Carl Dilthey ; F. Raine ; Heinrich Börnstein ; Charles L. Bernays ; Emil Rothe ; Eduard Leyh ; George Schneider ( who was also a banker ); Albert Sigel ; Franz Umbscheiden ; Edward Morwitz ( who was also a physician )

All theorems of ZFC are also theorems of von Neumann – Bernays – Gödel set theory, but the latter is, quite surprisingly, finitely axiomatized.

He also argues that the eventual outcome strongly resembles Edward Bernays vision for the " Democracity " during the 1939 New York World's Fair.

** The Bernays – Schönfinkel class ( also Bernays – Schönfinkel-Ramsey class )

Bernays also lectured on other areas of mathematics at the University of Göttingen.

Larry Tye describes in his book, " The Father of Spin: Edward L. Bernays & The Birth of PR ", some situations in twentieth-century America where tobacco and alcohol companies used techniques to make certain behaviors more socially acceptable.

This methodology was one of Edward Bernays ' favorite techniques for manipulating public opinion by the indirect use of " third-party authorities " to influence the public, without their conscious cooperation.

Public relations pioneer Edward Bernays later refined the creation and use of press releases.

Freud himself and his nephew Edward Bernays, who was the first to use psychological techniques in public relations, are discussed.

Bernays was one of the first to attempt to manipulate public opinion using the psychology of the subconscious.

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.

Another approach is taken by the von Neumann – Bernays – Gödel axioms ( NBG ); classes are the basic objects in this theory, and a set is then defined to be a class that is an element of some other class.

This was adopted by David Hilbert and Paul Bernays as the " contentual " finitist system for metamathematics, in which a proof of the consistency of other mathematical systems ( e. g. full Peano Arithmetic ) was to be given.

In 1929, Schönfinkel had one other paper published, on special cases of the decision problem (" Entscheidungsproblem "), that was prepared by Paul Bernays.

Unlike von Neumann – Bernays – Gödel set theory, where the axiom schema of Class Comprehension can be replaced with finitely many of its instances, Morse – Kelley set theory cannot be finitely axiomatized.

Ivy Lee and Edward Louis Bernays established the first definition of public relations in the early 1900s as

Edward Bernays, often described as the father of public relations

Edward Bernays ( 1891 – 1995 ), nephew of psychoanalyst Sigmund Freud, was considered the father of the field of public relations.

Edward Louis Bernays ( November 22, 1891 – March 9, 1995 ) was an Austrian-American pioneer in the field of public relations and propaganda, referred to in his obituary as " the father of public relations ".

Adam Curtis's award-winning 2002 documentary for the BBC, The Century of the Self, pinpoints Bernays as the originator of modern public relations, and Bernays was named one of the 100 most influential Americans of the 20th century by Life magazine.

According to the BBC interview with Bernays's daughter Anne, Bernays felt that the public's democratic judgment was " not to be relied upon " and he feared that " they American public could very easily vote for the wrong man or want the wrong thing, so that they had to be guided from above ".

As a genre of political thought, parallels exist between Niebuhr's " necessary illusions " and the " noble lies " of Leo Strauss, " public relations " of Edward Bernays and " myth making " of Niccolò Machiavelli.

Edward Bernays directed public relations of the fair in 1939, which he called ' democricity '.

His principal competitor in the new public relations industry was Edward Bernays.

To involve the politically reticent President Eisenhower, the UFC employed the public relations-and-advertising expert Edward L. Bernays to create, organise, and direct a psychologically inflammatory, anti – Communist disinformation campaign ( print and radio, film and television ) against the liberal Árbenz Government of Guatemala.

The public relations expert Edward L. Bernays manufactured the popular consent that made feasible the 1954 Guatemalan coup d ’ état by the United States.

In 1954, for his clients, the Eisenhower Administration and the United Fruit Company, the public relations expert Edward Bernays engineered American popular consent for the 1954 Guatemalan coup d ‘ état to overthrow a capitalist democracy in Central America.

NAM used pioneering public relations expert Edward Bernays in the 1930s to promote the benefits of capitalism, to combat the policies of President Roosevelt.

* Edward Bernays, a pioneer in public relations and later theorist of the importance of propaganda to democratic governance.

**** Edward Bernays ( 1891-1995 ), nephew of Sigmund Freud, great-grandson of Isaac Bernays and the " father of public relations "

** Lewis Adolphus Bernays ( 1831-1908 ), a public servant and agricultural writer in Australia ( son of Adolphus and a nephew of Isaac Bernays )

Modern advertising was created with the innovative techniques introduced with tobacco advertising in the 1920s, most significantly with the campaigns of Edward Bernays, which is often considered the founder of modern, Madison Avenue advertising.

This is the period in which modern advertising was introduced, most significantly with the innovative techniques developed by Edward Bernays in his campaigns for the tobacco industry.

If V is a standard model of ZFC and κ is an inaccessible in V, then: V < sub > κ </ sub > is one of the intended models of Zermelo – Fraenkel set theory ; and Def ( V < sub > κ </ sub >) is one of the intended models of Von Neumann – Bernays – Gödel set theory ; and V < sub > κ + 1 </ sub > is one of the intended models of Morse – Kelley set theory.

By applying this indexing to the Burali-Forti paradox we obtain another proof that the cardinal numbers are a proper class rather than a set, and ( at least in ZFC or in von Neumann – Bernays – Gödel set theory ) it follows from this that there is a bijection between the class of cardinals and the class of all sets.

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.

There is a most admirable monograph on the Chronicle by J. Bernays ( Berlin, 1861 ).

" Since the publication of I Bernays ' investigations there has been no doubt that this work is spurious.

In the foundations of mathematics, von Neumann – Bernays – Gödel set theory ( NBG ) is an axiomatic set theory that is a conservative extension of the canonical axiomatic set theory ZFC.

Those of Freud ’ s letters to his fianceé Martha Bernays which have been published contain a few hints about the course of Pappenheim ’ s therapy and Freud ’ s relationship to Breuer, but until all of Freud ’ s letters are published there is room for all kinds of speculation.

Clearly enough, Hilbert and Bernays do implicitly accept the potential infinite, but they claim that each induction in their proofs is finite.

* Von Neumann – Bernays – Gödel set theory is a conservative extension of Zermelo – Fraenkel set theory with the axiom of choice ( ZFC ).

Bernays is a surname and may refer to: