Axiomatization
Axiomatization In mathematics, axiomatization is the process of defining the basic ... mentioned in the example below. Example: The axiomatization of natural numbers The mathematical system of ...
http://en.wikipedia.org/wiki/Axiomatization - 3k - Cached - Similar pages

Talk:Axiomatization
Talk:Axiomatization Before my recent editing, the second-to ... an accurate description of the process of axiomatization in mathematics. Historical timeline? axiomatization of set theory? related fields? Rotem Dan ...
http://en.wikipedia.org/wiki/Talk:Axiomatization - 4k - Cached - Similar pages

Von Neumann–Bernays–Gödel set theory
... would, of course, be a large category. Axiomatization of NBG In this section we present an axiomatization of NBG (actually, two different ones, the ... refinement of the first). Compare with the axiomatization of Morse-Kelley set theory. We view ... NBG, but one which makes its formal axiomatization a bit mysterious, is that its axiom ... instances. Here we develop such a finite axiomatization, but with no guarantee that it ...
http://en.wikipedia.org/wiki/Von_Neumann–Bernays–Gödel_set_theory - 20k - Cached - Similar pages

Talk:Matiyasevich's theorem
... Matiyasevich's result: Corresponding to any given axiomatization of number theory, one can explicitly construct ... fact cannot be proved within the given axiomatization." Is there a logical mistake or could ... be given as: "Corresponding to any given axiomatization of number theory, there exists a Diophantine ... fact cannot be proved within the given axiomatization." ? MS 00:01, 03 Jun 2005 Nope ... imply we can prove within the given axiomatization that it has no solutions. Indeed, ...
http://en.wikipedia.org/wiki/Talk:Matiyasevich's_theorem - 5k - Cached - Similar pages

John von Neumann
... from obtaining the atomic bomb. Logic The axiomatization of mathematics, on the model of Euclid ... to itself. The problem of an adequate axiomatization of set theory was resolved implicitly about ... century: the sixth of these was the axiomatization of physical theories. Among the new physical ... satisfactory theoretical formulation. After having completed the axiomatization of set theory, von Neumann began to confront the axiomatization of QM. He immediately realized, in ...
http://en.wikipedia.org/wiki/John_von_Neumann - 57k - Cached - Similar pages

Talk:Peano axioms
... natural numbers cannot be excluded in any axiomatization. to Dedekind proved, in his 1888 book ... natural numbers cannot be excluded in any axiomatization; by the Lowenheim-Skolem theorem there exist ... should be changed to this particular(infinitary) axiomatization, because as it stands it is confusing ... a refernce to riogorous first order peano axiomatization? i want to see how is the ... then list them as a second-order axiomatization. However it's not a recent ...
http://en.wikipedia.org/wiki/Talk:Peano_axioms - 49k - Cached - Similar pages

User talk:Arthur Rubin
... want to put in (I wrote the axiomatization in the current article). von Neumann does ... your mother's set include a finite axiomatization of class comprehension (if it didn't ... my treatment, or to adapt my finite axiomatization section to your mother's axioms)? Randall ... axiom. Your mother did list a finite axiomatization under the axiom of constructibility, but did ...
http://en.wikipedia.org/wiki/User_talk:Arthur_Rubin - 35k - Cached - Similar pages

Talk:Naive set theory
... articles alongside the article with the formal axiomatization. What I object to is claims that ... antinomies are mentioned, should not assert that axiomatization is the solution, but should mention that ... consider them to have been solved by axiomatization, others by the cumulative hierarchy. History. Try ... a sense of a normative preference for axiomatization; an implication will remain that non-axiomatic ...
http://en.wikipedia.org/wiki/Talk:Naive_set_theory - 95k - Cached - Similar pages

Dynamic logic
... follows, taking as already given a suitable axiomatization of modal logic including such axioms for ... which one takes as primitive. An alternative axiomatization would have been to take the theorems ... In 1978 Krister Segerberg found a complete axiomatization of PDL, namely any complete axiomatization of modal logic K together with axioms ...
http://en.wikipedia.org/wiki/Dynamic_logic - 31k - Cached - Similar pages

Halting problem
... asserting that a complete, consistent and sound axiomatization of all statements about natural numbers is ... that we have a consistent and complete axiomatization of all true first-order logic statements ... statement, say H(a, i). Since the axiomatization is complete it follows that either there ... that there is a consistent and complete axiomatization of all true first-order logic statements ...
http://en.wikipedia.org/wiki/Halting_problem - 59k - Cached - Similar pages