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Axiom schema
In symbolic logic, it is sometimes inconvenient or impossible to express an axiomatic system in a finite number of axioms. For this reason, an axiom schema is used. Formally, an axiom schema is a set (usually infinite) of well formed formulae, each of which is taken to be an axiom. Often, this set is constructed recursively. A well known axiom schema is the axiom schema of replacement.
There is debate among metamathematicians as to whether an axiomatic system containing an axiom schema should be considered elegant. Some logicians thus prefer, if possible, to use a finite number of axioms.
03-10-2013 05:06:04
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details