An order-theoretic characterization of the Howard-Bachmann-hierarchy

DOI10.1007/s00153-016-0515-6zbMath1421.03005arXiv1411.4481OpenAlexW2243196114WikidataQ59890201 ScholiaQ59890201MaRDI QIDQ512137

Andreas Weiermann, Michael Rathjen, Jeroen Van der Meeren

Publication date: 24 February 2017

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4481

zbMATH Keywords

independence resultsKruskal's theoremcollapsing functionHoward-Bachmann numberimpredicative theorymaximal order typeminimal bad sequencenatural well-orderingsordinal notation systemsproof-theoretical ordinalrecursively defined treestree-embeddabilitieswell-partial-orderings

Mathematics Subject Classification ID

Partial orders, general (06A06) Cut-elimination and normal-form theorems (03F05) Consistency and independence results (03E35) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Proof theory in general (including proof-theoretic semantics) (03F03) Recursive ordinals and ordinal notations (03F15) Ordinal and cardinal numbers (03E10)

Related Items

Minimal bad sequences are necessary for a uniform Kruskal theorem, Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition, Bachmann-Howard derivatives, PROOF-THEORETIC STRENGTHS OF WEAK THEORIES FOR POSITIVE INDUCTIVE DEFINITIONS, A flexible type system for the small Veblen ordinal, From Kruskal’s theorem to Friedman’s gap condition

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