In mathematical logic, more specifically in the proof theory of first-order theories, an extension by definition formalizes the introduction of a new symbol by means of a definition. For example, it is common in naive set theory to introduce a symbol ∅ {\displaystyle \emptyset } for the set that has no member.
In mathematical logic, more specifically in the proof theory of first-order theories, an extension by definition formalizes the introduction of a new symbol by means of a definition. For example, it is common in naive set theory to introduce a symbol ∅ {\displaystyle \emptyset } for the set that has no member.
Source: Wikipedia "Extension by definition" · CC BY-SA 4.0
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