first-order structure

结构

Foundations & Logic · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: L-structure

Translation evidence: Literature usage

Meaning in context

A nonempty domain equipped with interpretations of a first-order language’s constants, functions and relations of the prescribed arities.

非空论域连同一阶语言中各常数、函数和关系符号的符合元数的解释。

Example

(Z,0,+,<)(\mathbb Z,0,+,<) interprets an ordered additive language.

Usage and distinctions

A structure becomes a model of a theory only if it satisfies that theory’s sentences.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§10.2 Truth in a Model; §10.4 Validity and Logical Consequence; §10.5 Soundness and Completeness · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，第14讲PDF p.19「结构」 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.