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...

Geometry) published by Hilbert in 1899 proposes a formal set, called Hilbert's axioms, substituting for the traditional axioms of Euclid. They avoid weaknesses...

set of axioms for Euclidean geometry such as Hilbert's axioms or another modern equivalent (Faber 1983, p. 131). Euclid's original set of axioms is ambiguous...

basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead. In Euclid's Elements, the first 28...

axiom Axiom of constructibility Rank-into-rank Kripke–Platek axioms Diamond principle Parallel postulate Birkhoff's axioms (4 axioms) Hilbert's axioms (20...

many axioms. The axiom system is due to Alfred Tarski who first presented it in 1926. Other modern axiomizations of Euclidean geometry are Hilbert's axioms...

Euclidean or non-Euclidean. Hilbert's axioms: Hilbert's axioms had the goal of identifying a simple and complete set of independent axioms from which the most...

such as groups). Thus non-logical axioms, unlike logical axioms, are not tautologies. Another name for a non-logical axiom is postulate. Almost every modern...

Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed...

Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's...

axioms, Pasch's axiom can be proved as a theorem; it is a consequence of the plane separation axiom when that is taken as one of the axioms. Hilbert uses...

numbers n. Hilbert's axiomatic system is different. At the outset it declares its axioms, and any (arbitrary, abstract) collection of axioms is free to...

still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and...

geometrical axioms. ... On the other hand a direct method is needed for the proof of the compatibility of the arithmetical axioms." Hilbert's statement...

mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...

Euclidean geometry Euclidean space Foundations of geometry Hilbert's axioms Tarski's axioms Birkhoff, George David (1932), "A Set of Postulates for Plane...

of attempting to define them, their interplay is ruled (in Hilbert's axiom system) by axioms like "For every two points there exists a line that contains...

ISBN 0-674-32449-8. Hilbert's 1927, Based on an earlier 1925 "foundations" lecture (pp. 367–392), presents his 17 axioms -- axioms of implication #1-4, axioms about...

universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first...

satisfy the Wightman axioms. Haag–Kastler axioms Hilbert's sixth problem Axiomatic quantum field theory Local quantum field theory "Hilbert's sixth problem"...

vertices of a triangle. Euclid's Elements Foundations of geometry Hilbert's axioms Saccheri quadrilateral (considered earlier than Saccheri by Omar Khayyám)...

four axioms that at least one parallel line exists given a line L and a point P not on L, as follows: Construct a perpendicular: Using the axioms and previously...

equivalence relation on lines. Incidence geometry Euclidean geometry Hilbert's axioms Tarski's axioms Affine geometry Absolute geometry Non-Euclidean geometry Erlangen...

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...

content. Today's student of geometry has axioms other than Euclid's available: see Hilbert's axioms and Tarski's axioms. Ernst Kötter published a (German) report...

notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. His work on axiom systems is considered one of the starting points...

Hilbert–Serre theorem Hilbert–Smith conjecture Hilbert–Speiser theorem Hilbert–Waring theorem Hilbert's arithmetic of ends Hilbert's axioms Hilbert's basis theorem...

rather easy to prove that all definitions of Euclidean spaces satisfy Hilbert's axioms, and that those involving real numbers (including the above given definition)...

Pythagorean field satisfies many of Hilbert's axioms, such as the incidence axioms, the congruence axioms and the axioms of parallels. However, in general...

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive...