Difference between revisions of "Axiom schema"
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In [[mathematical logic]], an '''axiom schema''' (plural: '''axiom schemata''') generalizes the notion of [[axiom]]. | In [[mathematical logic]], an '''axiom schema''' (plural: '''axiom schemata''') generalizes the notion of [[axiom]]. | ||
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| + | == Formal definition == | ||
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| + | An axiom schema is a [[Well-formed formula|formula]] in the language of an [[axiomatic system]], in which one or more [[Metavariable|schematic variables]] appear. | ||
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| + | These variables, which are metalinguistic constructs, stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions. Often, such conditions require that certain variables be free, or that certain variables not appear in the subformula or term. | ||
== See also == | == See also == | ||
Revision as of 09:49, 13 September 2016
In mathematical logic, an axiom schema (plural: axiom schemata) generalizes the notion of axiom.
Formal definition
An axiom schema is a formula in the language of an axiomatic system, in which one or more schematic variables appear.
These variables, which are metalinguistic constructs, stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions. Often, such conditions require that certain variables be free, or that certain variables not appear in the subformula or term.
See also
- Axiom
- Axiom schema of predicative separation
- Axiom schema of replacement
- Axiom schema of specification
- Mathematical logic
External links
- Axiom schema @ Wikipedia.org
