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

The Hilbert–Bernays paradox is a distinctive paradox belonging to the family of the paradoxes of reference (like Berry's paradox). It is named after David...

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...

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...

infinitely many axioms added (these can be easily formalized as an axiom schema): ∃ x 1 : ∃ x 2 : ¬ ( x 1 = x 2 ) {\displaystyle \exists x_{1}:\exists x_{2}:\lnot...

In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive...

mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage...

are often formulated as schemata employing metavariables. In the rule (schema) above, the metavariables A and B can be instantiated to any element of...

problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers...

it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. Waring's problem has its own Mathematics Subject...

The Brouwer–Hilbert controversy (German: Grundlagenstreit, lit. 'foundational debate') was a debate in twentieth-century mathematics over fundamental...

theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics...

independently proposed replacing the axiom schema of specification with the axiom schema of replacement. Appending this schema, as well as the axiom of regularity...

variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was...

metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of...

property. Considered as an axiomatic principle, it is called the axiom schema of set induction. The principle implies transfinite induction and recursion...

Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent...

The T-schema ("truth schema", not to be confused with "Convention T") is used to check if an inductive definition of truth is valid, which lies at the...

Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen. At...

and replacing the second-order induction axiom with a first-order axiom schema. The term Peano arithmetic is sometimes used for specifically naming this...

Axiomatizing arithmetic induction in first-order logic requires an axiom schema containing a separate axiom for each possible predicate. The article Peano...

Parallel postulate Birkhoff's axioms (4 axioms) Hilbert's axioms (20 axioms) Tarski's axioms (10 axioms and 1 schema) Axiom of Archimedes (real number) Axiom...

a point and a line. Hilbert uses two axioms of Continuity, and they require second-order logic. By contrast, Tarski's Axiom schema of Continuity consists...

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...

vectors ('states') in a separable Hilbert space, and physical quantities as linear operators that act in this Hilbert space. This approach is fully falsifiable...

This article contains a list of sample Hilbert-style deductive systems for propositional logics. Classical propositional calculus is the standard propositional...

into a set theory with classes. First, the axiom schema of class comprehension is added. This axiom schema states: For every formula ϕ ( x 1 , … , x n )...

paradox in 1902. If the axiom schema of unrestricted comprehension is weakened to the axiom schema of specification or axiom schema of separation, If P is a...

that formalists, such as David Hilbert (1862–1943), hold that mathematics is only a language and a series of games. Hilbert insisted that formalism, called...

logic and first-order logic. The deduction theorem is an important tool in Hilbert-style deduction systems because it permits one to write more comprehensible...