1. The study of the structure, properties, and foundations of mathematical systems and formal logic, including the analysis of mathematical proofs and axioms.
Usage: technical; academic; typically used in singular form; field-specific to mathematics and logic

Examples

• Metamathematics examines whether mathematical systems are consistent and complete.
• Gödel's incompleteness theorems are fundamental results in metamathematics.
• The researcher specialized in metamathematics and the foundations of set theory.
• Metamathematics helps us understand the limits and capabilities of formal mathematical reasoning.
• Questions about the decidability of mathematical problems fall within the scope of metamathematics.