Ordinal notation system: Difference between revisions

An '''ordinal notation system''' (also called an '''ordinal notation''' informally) is a system of names for ordinals, or equivalently, a well-ordered set of objects that "can be considered names". There may not be a formal restriction of what objects can be considered names, but most common examples include strings, sequences of other such objects, trees/hydras, and terms built up from constants and functions. Most authors also require the well-order to be recursive, and this requirement is included in the definition of proof-theoretic ordinals that uses ordinal notation systems.