first-order sentence

语句

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

Other names / variants: sentence

Translation evidence: Literature usage

Meaning in context

A formula of a first-order language with no free variable occurrences.

一阶语言中不含自由变元出现的公式。

Example

∀x  (x=x)\forall x\;(x=x) is a sentence; x=xx=x is an open formula.

Usage and distinctions

A sentence may be false in a structure; being closed does not mean being a theorem.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§7.2 The Universal Quantifier; §7.3 The Existential Quantifier · Checked 2026-10-14

Translation sources

  1. 杨睿之（复旦大学）— 数理逻辑，2021年秋季PDF p.20：「语句（sentence）」及没有自由出现的定义 · Checked 2026-10-14
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