An atomic first-order formula is a relation applied to terms, or a logical equality of two terms when logical equality is included in the logic. It contains no logical connective or quantifier. Its truth is preserved and reflected by an embedding of first-order structures.
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An atomic formula, in the context of formal logic and mathematical logic, is a basic type of formula that expresses a simple statement or proposition about a specific relation or property without any logical connectives (such as AND, OR, NOT, etc.). An atomic formula typically consists of: 1. **Predicate Symbols**: These are symbols that represent properties or relations.