# Definitions for axiom schemaax·iom schema

### Wiktionary(0.00 / 0 votes)Rate this definition:

1. 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.

### Freebase(0.00 / 0 votes)Rate this definition:

1. 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

1. Chaldean Numerology

The numerical value of axiom schema in Chaldean Numerology is: 3

2. Pythagorean Numerology

The numerical value of axiom schema in Pythagorean Numerology is: 3

## Translations for axiom schema

• 公理模式

### Translation

#### Find a translation for the axiom schema definition in other languages:

Select another language:

• - Select -
• 简体中文 (Chinese - Simplified)
• 繁體中文 (Chinese - Traditional)
• Español (Spanish)
• Esperanto (Esperanto)
• 日本語 (Japanese)
• Português (Portuguese)
• Deutsch (German)
• العربية (Arabic)
• Français (French)
• Русский (Russian)
• ಕನ್ನಡ (Kannada)
• 한국어 (Korean)
• עברית (Hebrew)
• Gaeilge (Irish)
• Українська (Ukrainian)
• اردو (Urdu)
• Magyar (Hungarian)
• मानक हिन्दी (Hindi)
• Indonesia (Indonesian)
• Italiano (Italian)
• தமிழ் (Tamil)
• Türkçe (Turkish)
• తెలుగు (Telugu)
• ภาษาไทย (Thai)
• Tiếng Việt (Vietnamese)
• Čeština (Czech)
• Polski (Polish)
• Bahasa Indonesia (Indonesian)
• Românește (Romanian)
• Nederlands (Dutch)
• Ελληνικά (Greek)
• Latinum (Latin)
• Svenska (Swedish)
• Dansk (Danish)
• Suomi (Finnish)
• فارسی (Persian)
• ייִדיש (Yiddish)
• հայերեն (Armenian)
• Norsk (Norwegian)
• English (English)

### Word of the Day

#### Would you like us to send you a FREE new word definition delivered to your inbox daily?

Please enter your email address:

## Citation

#### Use the citation below to add this definition to your bibliography:

Style:MLAChicagoAPA

"axiom schema." Definitions.net. STANDS4 LLC, 2021. Web. 2 Dec. 2021. <https://www.definitions.net/definition/axiom+schema>.

## Are we missing a good definition for axiom schema? Don't keep it to yourself...

### Add to Chrome

Get instant definitions for any word that hits you anywhere on the web!

### Add to Firefox

Get instant definitions for any word that hits you anywhere on the web!

»
• A. caddie
• B. huff
• C. descant
• D. suffuse