A fundamental sequence (FS) is an important concept in the study of ordinal hierarchies. If \(\alpha\) is a countable limit ordinal, a fundamental sequence for \(\alpha\) is a monotonically increasing sequence of length \(\omega\) consisting of ordinals, supremum of which is equal to \(\alpha\). Due to poor standardization in set theory, definitions of valid FS's vary. Some authors use "least strict upper bound" instead of "supremum," some relax the monotonicity condition to only require nondecreasing sequences, and some even allow fundamental sequences for successor ordinals.