Berry's paradox). It is named after David Hilbert and Paul Bernays. The paradox appears in Hilbert and Bernays' Grundlagen der Mathematik and is used by...

David Hilbert. Bernays was born into a distinguished German-Jewish family of scholars and businessmen. His great-grandfather, Isaac ben Jacob Bernays, served...

facsimile on the left-hand sides. The Hilbert Bernays Project is producing an English translation. Hilbert–Bernays paradox Sieg, Wilfried; Ravaglia, Mark (2005)...

Keen refers to. Hilbert–Bernays paradox Insolubilia Knights and Knaves Performative contradiction Self-reference Epimenides paradox has "All Cretans are...

itself", a heterological word? (A close relative of Russell's paradox.) Hilbert–Bernays paradox: If there was a name for a natural number that is identical...

Hilbert's chair when he retired in 1930), Emmy Noether and Edmund Landau. One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in...

system Hilbert–Bernays paradox Hilbert–Bernays provability conditions Hilbert–Burch theorem Hilbert–Kunz function Hilbert–Poincaré series Hilbert–Pólya...

Professor Hilbert among others. Frege sent a copy of his Grundgesetze der Arithmetik to Hilbert; as noted above, Frege's last volume mentioned the paradox that...

description Hilbert–Bernays paradox – limit of classical logicPages displaying wikidata descriptions as a fallback Interesting number paradox – On the smallest...

class and set. Paul Bernays reformulated von Neumann's theory by taking class and set as primitive notions. Kurt Gödel simplified Bernays' theory for his...

theorem assumes that the provability predicate ProvA(P) satisfies the Hilbert–Bernays provability conditions. Letting #(P) represent the Gödel number of...

declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size...

Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as...

the definition of the cardinality of a set. See Hilbert's paradox of the Grand Hotel for more on paradoxes of enumeration. "I see it but I don't believe...

intuitionism as a challenge to the prevailing formalism of David Hilbert and his colleagues, Paul Bernays, Wilhelm Ackermann, John von Neumann, and others. As a...

V_{\alpha }} and ∪ x ∈ V α + 1 {\displaystyle \cup x\in V_{\alpha +1}} . Hilbert's paradox implies that no set with the above properties exists . For suppose...

cases of the decision problem, that was prepared by Paul Bernays. As late as 1930, Hilbert believed that there would be no such thing as an unsolvable...

a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann...

26) The debate had a profound effect on Hilbert. Reid indicates that Hilbert's second problem (one of Hilbert's problems from the Second International...

nor for unrestricted comprehension, thereby avoiding Russell's paradox. Von Neumann–Bernays–Gödel set theory (NBG) is a commonly used conservative extension...

p. 396 In his 1930–1931 The Philosophy of Mathematics and Hilbert's Proof Theory Bernays asserts (in the context of rebutting Logicism's construction...

of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities...

announced by Paul Bernays in 1941, although he did not publish a proof until 1954. The proof involves (and led to the study of) Rieger-Bernays permutation models...

Mathematik" (Hilbert & Bernays 1934), Bernays wrote the following, which is reminiscent of the famous note by Frege when informed of Russell's paradox. "Die...

In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent...

hypothetical statement: "if the premises hold, then the conclusion holds." In a Hilbert system, the premises and conclusion of the inference rules are simply formulae...

After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems...

Ausarbeitung von Paul Bernays (Edited and with an English introduction by David E. Rowe), Basel, Birkhauser (1992). Weyl 1927 Comments on Hilbert's second lecture...

Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox arises from...

Medal, the highest honor it can confer for work in mathematics. David Hilbert defended it from its critics by declaring, "No one shall expel us from...