What does axiom schema mean?
Definitions for axiom schema
ax·iom schema
This dictionary definitions page includes all the possible meanings, example usage and translations of the word axiom schema.
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Wiktionary
axiom schemanoun
A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
Wikipedia
Axiom schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
Wikidata
Axiom schema
In mathematical logic, an axiom schema generalizes the notion of axiom. 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. Given that the number of possible subformulas or terms that can be inserted in place of a schematic variable is countably infinite, an axiom schema stands for a countably infinite set of axioms. This set can usually be defined recursively. A theory that can be axiomatized without schemata is said to be finitely axiomatized. Theories that can be finitely axiomatized are seen as a bit more metamathematically elegant, even if they are less practical for deductive work. Two very well known instances of axiom schemata are the: ⁕Induction schema that is part of Peano's axioms for the arithmetic of the natural numbers; ⁕Axiom schema of replacement that is part of the standard ZFC axiomatization of set theory.
Numerology
Chaldean Numerology
The numerical value of axiom schema in Chaldean Numerology is: 3
Pythagorean Numerology
The numerical value of axiom schema in Pythagorean Numerology is: 3
Translations for axiom schema
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- 公理模式Chinese
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"axiom schema." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/axiom+schema>.
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