Kripke-Platek axioms (1990 bytes)
1: ...t-order logic]]; it has an [[infinite]] number of axioms because an [[axiom schema]] is used.
3: The axioms of KP are:

Saul Kripke (7437 bytes)

Kripke semantics (26124 bytes)
105: A list of common modal axioms together with their
107: the axioms often varies.
161: !name!!axioms!!frame condition
252: The axioms ''T'', ''4'', ''D'', ''B'', ''5'', ''3'', ''2'' (...
265: ...is is a very powerful criterion; for example, all axioms

Wightman axioms (13769 bytes)
1: ...f generality because we can think of the Wightman axioms as describing the superselection sector of the va...
61: the axioms - that energy-momentum spectrum has a gap between...
65: From these axioms, certain general theorems follow:
69: ...g certain set of properties which follow from the axioms, are sufficient to reconstruct the field theory -...
75: ... is a million dollar prize for a proof that these axioms can be satisfied for [[gauge theories]], with the...

List of axioms (2010 bytes)
1: ...; see [[axiom]] and [[self-evidence]]. Individual axioms are almost always part of a larger [[axiomatic sy...
3: ==[[Zermelo-Frankel axioms]]==
4: ''These are the'' de facto ''standard axioms for contemporary [[mathematics]]''
20: ''With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most...
36: ==Other axioms of [[mathematical logic]]==

Probability axioms (4568 bytes)
1: ...y that <math>P</math> must satisfy the Kolmogorov axioms.
11: == Kolmogorov axioms ==
13: ...owing three axioms are known as the '''Kolmogorov axioms''', after [[Andrey Kolmogorov]] who developed the...
39: From the Kolmogorov axioms one can deduce other useful rules for calculating...

Peano axioms (13723 bytes)
1: ...ental formalism for [[arithmetic]], and the Peano axioms form a basis for the formalisation of stronger th...
3: Using the Peano axioms, one can construct many of the most important [[n...
5: ==The axioms==
7: Informally, the Peano axioms may be stated as follows:
25: The Peano axioms can be summed up by the following diagram:

Birkhoff's axioms (1982 bytes)
1: ...geometry]] sometimes referred to as '''Birkhoff's axioms'''. These postulates are all based on basic [[geo...

Hilbert's axioms (5211 bytes)
1: ... modern treatment of [[Euclidean geometry]]. The axioms were originally published in ''Grundlagen der Geo...
4: ===I. Axioms of Incidence===
26: ===II. Axioms of Order===
38: ===III. Axioms of Congruence===
57: ===V. Axioms of Continuity===

History of the separation axioms (4512 bytes)
5: ...assumed (what we now think of as) some separation axioms. For example, the definition given by [[Felix Hau...
7: ... fact, studying spaces that satisfy only ''some'' axioms helps build up to the notion of full metrisabilit...
9: ... were first studied together in this way were the axioms for [[accessible space]]s, [[Hausdorff space]]s, ...
15: ...sub>1</sub>, and T₂. But for the other axioms, different authors could use radically different ...
19: ...ume T₁, so they studied the separation axioms in the greatest generality from the beginning. Th...

Kuratowski closure axioms (2216 bytes)
2: ...hes of [[mathematics]], the '''Kuratowski closure axioms''' is a set of [[axiom]]s that allows one to defi...
7: The closure operator satisfies the following axioms:
21: Similar sets of axioms exist for other operators.
23: Axioms (3) and (4) can be generalised (using a proof by ...
28: An operator that satisfies only axioms (1) and (2) is called a ''[[Moore closure]]''. M...

Huzita's axioms (8820 bytes)
1: ...l known set of [[axiom]]s related to origami. The axioms are as follows:

Von Neumann-Bernays-Gödel axioms (1505 bytes)
2: ... yield the same results as the [[Zermelo-Fraenkel axioms]] (ZF) , but in a more logically elegant fashion.
6: ...961]], it is not possible to find a finite set of axioms that is logically equivalent to ZF; the language ...

Kripkenstein (1177 bytes)

KP (666 bytes)
11: *[[Kripke-Platek set theory]] is the theory of admissible sets.

Arthur Wightman (396 bytes)
3: ...ld theory]], and originated the set of [[Wightman axioms]].
6: * [[Wightman axioms|Streater-Wightman axioms]]
7: * [[Garding-Wightman axioms]]

Intermediate logics (1094 bytes)
7: ...iate logics, often obtained by adding one or more axioms to [[intuitionistic logic]].
8: Examples of such axioms are:

ZF (200 bytes)
4: * The [[Zermelo-Fraenkel axioms]], a system of axioms in mathematical [[set theory]].

Inner model (1563 bytes)
15: ...ZFC (like [[Zermelo-Frankel set theory| ZF]] or [[Kripke-Platek set theory|KP]]) as well.

Axiomatization (1807 bytes)
4: Usually these axioms are not mentioned when a mathematical equation is
5: ...thematical theories usually are based on very few axioms. Some of them are mentioned in the example below.
8: ...] in [[1901]]. He defined the axioms (see [[Peano axioms]]) for the set N of natural numbers as being:
16: ...atics sometimes assert that mathematicians choose axioms "arbitrarily", but the truth is that although the...

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