Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/224563
Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
Hardy functions are defined by transfinite recursion and provide upper bounds
for the growth rate of the provably total computable functions in various formal
theories, making them an essential ingredient in many proofs of independence. Their
definition is contingent on a choice of fundamental sequences, which approximate
limits in a ‘canonical’ way. In order to ensure that these functions behave as
expected, including the aforementioned unprovability results, these fundamental
sequences must enjoy certain regularity properties.
In this article, we prove that Buchholz’s system of fundamental sequences for the ϑ
function enjoys such conditions, including the Bachmann property. We partially
extend these results to variants of the ϑ function, including a version without
addition for countable ordinals. We conclude that the Hardy functions based on
these notation systems enjoy natural monotonicity properties and majorize all
functions defined by primitive recursion along ϑ(εΩ+1).
Matèries (anglès)
Citació
Col·leccions
Citació
FERNÁNDEZ DUQUE, David, WEIERMANN, Andreas. Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal. _Annals of Pure and Applied Logic_. 2024. Vol. 175, núm. 8. [consulta: 26 de febrer de 2026]. ISSN: 0168-0072. [Disponible a: https://hdl.handle.net/2445/224563]