Weak Completeness in Logic
Weak completeness states that if a statement is semantically valid (true in…
Metatheory
Metatheory involves the theoretical analysis of mathematical and logical systems. It examines…
Metatheorem: Understanding Theorems About Theories
A metatheorem is a theorem that describes properties of a formal system,…
Metamathematics
Metamathematics examines mathematical systems and theories from an elevated viewpoint, employing principles…
Metalogic: Understanding the Foundations of Logic
Metalogic explores the inherent properties of formal logical systems and languages. It…
Gödel’s Incompleteness Theorems
Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that…
Finitely Axiomatizable Theories
A theory is finitely axiomatizable if it can be completely defined by…