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...tated in the language of [[category theory]], as Leinster pointed out, the axioms can be stated without references to category theory. == Axioms == ...

In [[mathematical physics]], the '''Dirac–von Neumann axioms''' give a [[mathematical formulation of quantum mechanics]] in terms of [[linear operator|operator]] The Dirac–von Neumann axioms can be formulated in terms of a [[C*-algebra]] as follows. ...

{{Short description|Mathematical problem}} ...]], and [[exponentiation]] over the positive [[integer]]s that cannot be [[mathematical proof|proved]] using eleven [[axiom]]s about these operations that are taug ...

...ternary operation]] <math>\langle x,y,z \rangle</math> satisfying a set of axioms which generalise the notions of medians of triples of real numbers and of t The axioms are ...

...and is the basis for the characterization of the concept of {{em|size}} in mathematical morphology. Let ''X'' be a [[Set (mathematics)|set]] (i.e., a [[binary image]] in mathematical morphology), and consider the series of sets <math>\{\gamma_k(X)\}</math>, ...

In mathematical set theory, the '''axiom of adjunction''' states that for any two sets ''x' ...c=page 68, axiom II (2)}} introduced the axiom of adjunction as one of the axioms for a system of set theory that he introduced in about 1929. ...

In [[mathematical logic]], '''basic fuzzy logic''' (or shortly '''BL'''), the logic of the [[ === Axioms === ...

==Relation to other axioms== ...ology | series=Contemporary Mathematics | volume=84 | publisher=[[American Mathematical Society]] | location=Providence, RI | year=1989 | isbn=0-8218-5091-1 | url- ...

{{Short description|System of mathematical set theory}} ...iated [[iterative hierarchy]]. '''S''' has the important property that all axioms of [[Zermelo set theory]] ''Z'', except the [[axiom of extensionality]] and ...

...ng the Four Principal Types of Order |journal=Transactions of the American Mathematical Society |volume=38 |issue=1 |pages=1–9 |doi=10.1090/S0002-9947-1935-1501800 ===Axioms=== ...

...-1940-0002894-7/home.html Polyadic groups], ''Transactions of the American Mathematical Society'' 48 (1940), 208&ndash;350.</ref> ==Axioms== ...

...h>L, R</math>, and <math>e</math> are constants satisfying the following [[axioms]] for all <math>x,y,z</math> in its [[Domain of discourse|universe]]: [[Category:Mathematical logic]] ...

== Axioms of Q₀ == The system has just five axioms, which can be stated as: ...

...& Tversky, 1971), which Krantz and Tversky wrote in collaboration with the mathematical psychologist [[R. Duncan Luce]] and philosopher [[Patrick Suppes]]. Krantz ...proposed a general schema to ascertain the sufficient set of cancellation axioms for a class of polynomial combination rules he called ''simple polynomials' ...

These axioms thus have the respective types: The axioms UIP and K are equivalent.{{r|nlab-set-truncation}} Indeed, K is a special c ...

...rties of 0,&nbsp;1,&nbsp;+,&nbsp;×,&nbsp;<math>x^y</math>, together with [[mathematical induction|induction]] for formulas with [[bounded quantifier]]s. ...much of ordinary mathematics that can be stated in the language of [[Peano axioms|first-order arithmetic]]. ...

...ts such as assignment, iteration and composition instructions and from the axioms of the [[data structure]]s in question see {{harvtxt|Mirkowska|Salwicki|198 The following diagram helps to locate algorithmic logic among other [[Mathematical logic|logics]]. ...

...ooks.google.com/books?id=eUmDAwAAQBAJ&pg=PA18|year=2011|publisher=American Mathematical Soc.|isbn=978-0-8218-5195-1|page=18}}</ref><ref>{{cite arXiv|last1=Ayala|fi ...[Eilenberg–Steenrod axioms]] for homology theories. The Eilenberg–Steenrod axioms state that a homology theory is uniquely determined by its value for the po ...

...ical axioms at all.<ref>{{Cite book| last1=Monk | first1=J. Donald | title=Mathematical Logic | publisher=[[Springer-Verlag]] | location=Berlin, New York | series= ...ories and Automata on Infinite Trees |journal=Transactions of the American Mathematical Society |date=July 1969 |volume=141 |pages=1–35 |doi=10.2307/1995086|jstor= ...

...ted by [[Giuseppe Peano]] in 1889 as the basis for his arithmetic ([[Peano Axioms]]). He introduced the class term, which formally correctly describes classe ...tended as an alternative to Zermelo-Fraenkel. In 1940 Quine advanced NF to Mathematical Logic (ML). Since the [[antinomy]] of [[Burali-Forti]] was derived in the f ...