Concept

Elementary class

Overview

In model theory, a branch of mathematical logic, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first-order theory.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Related ideas

• First-order logic
• Compactness theorem
• Mathematical logic
• Model theory
• Structure (mathematical logic)
• Cardinality
• Signature (logic)

Opposing perspectives

• First-order logic
• Gödel's completeness theorem
• Compactness theorem
• Second-order logic

Place in the tradition

Part of First-order logic.

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