2015/12/16 by Fedor Pakhomov, Pakhomov, Fedor
Computer Science · Mathematics · #03F15 #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.LO #msc:03F15
paper · pdf · doi:10.48550/arxiv.1512.05036
15 pages
arxiv created 2015/12/16 · openalex publication_date 2015/12/16 · arxiv updated 2015/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Caucal hierarchy is a well-known class of graphs with decidable monadic theories. It were proved by L. Braud and A. Carayol that well-orderings in the hierarchy are the well-orderings with order types less than ε0. Naturally, every well-ordering from the hierarchy could be considered as a constructive system of ordinal notations. In proof theory constructive systems of ordinal notations with fixed systems of cofinal sequences are used for the purposes of classification of provable recursive functions of theories. We show that any well-ordering from the hierarchy could be extended by a monadically definable system of cofinal sequences with Bachmann property. We show that the growth speed of functions from fast-growing hierarchy based on constructive ordinal notations from Caucal hierarchy may be only slightly influenced by the choice of monadically definable systems of cofinal sequences. We show that for ordinals less than ωω a fast-growing hierarchy based on any system of ordinal notations from Caucal hierarchy coincides with Löb-Wainer hierarchy.