List of axioms information

Individual axioms are almost always part of a larger axiomatic system. Together with the axiom of choice (see below), these are the de facto standard axioms for...

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...

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

sets of axioms for projective geometry have been proposed (see for example Coxeter 2003, Hilbert & Cohn-Vossen 1999, Greenberg 1980). These axioms are...

axiom of choice for their proofs. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, such as the axiom of...

probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central...

This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...

of logic. The theorems are the logical consequences of the axioms, that is, the statements that can be obtained from the axioms by using the laws of deductive...

a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list...

mathematically. List of algorithms List of axioms List of conjectures List of conjectures by Paul Erdős Combinatorial principles List of equations List of formulae...

axiom, first investigated by Kurt Gödel, is inconsistent with the proposition that zero sharp exists and stronger large cardinal axioms (see list of large...

with certain properties. Without such an axiom, such a set might not provably exist. Important countability axioms for topological spaces include: sequential...

Zermelo–Fraenkel axioms (but not the axiom of extensionality, the axiom of regularity, or the axiom of choice) then became necessary to make up for some of what was...

geometry Analytic geometry Birkhoff's axioms Cartesian coordinate system Hilbert's axioms Incidence geometry List of interactive geometry software Metric...

of logic, mathematics, and computer science that use it, the axiom of extensionality, axiom of extension, or axiom of extent, is one of the axioms of...

separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are not fundamental axioms like those...

variety is a class of algebraic structures that share the same operations, and the same axioms, with the condition that all axioms are identities. What...

proven (principle of explosion). In an axiomatic system, an axiom is called independent if it cannot be proven or disproven from other axioms in the system...

whose axioms are true for the natural numbers cannot prove all first-order statements true for the natural numbers, even if the list of axioms is allowed...

the axiom schema of replacement with that of separation; General set theory, a small fragment of Zermelo set theory sufficient for the Peano axioms and...

instances of axiom schemata are the: induction schema that is part of Peano's axioms for the arithmetic of the natural numbers; axiom schema of replacement...