Ordinal logics

Ordinal logics are a way to understand the foundations of mathematics by using a hierarchy of abstract "steps" or levels, called ordinals, to organize truths and proofs. They help mathematicians analyze which statements can be proven within a system and how these systems can grow in strength. Think of it as a structured ladder where each rung represents a more powerful or complex logical system, enabling us to address questions dependent on the boundaries of what can be formally proven. This approach helps in exploring the limits and capabilities of mathematical reasoning.