The Veblen functions for computability theorists

DOI10.2178/jsl/1305810765zbMath1220.03050arXiv0910.5442OpenAlexW3106208063MaRDI QIDQ3011121

Alberto Marcone, Antonio Montalbán

Publication date: 28 June 2011

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.5442

zbMATH Keywords

ACAreverse mathematicscomputabilityordinal analysisjumpcomputable linear orderingarithmetical comprehensioncomputable ordinalomega jump

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Recursive ordinals and ordinal notations (03F15) Theory of numerations, effectively presented structures (03D45) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

Related Items (22)

Well-Ordering Principles in Proof Theory and Reverse Mathematics ⋮ THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS ⋮ Derivatives of normal functions and \(\omega \)-models ⋮ Reducing ω-model reflection to iterated syntactic reflection ⋮ Turing reducibility in the fine hierarchy ⋮ Well ordering principles for iterated \(\Pi^1_1\)-comprehension ⋮ A note on ordinal exponentiation and derivatives of normal functions ⋮ PREDICATIVE COLLAPSING PRINCIPLES ⋮ On the logical strength of the better quasi order with three elements ⋮ Functorial Fast-Growing Hierarchies ⋮ The Π21$\Pi ^1_2$ consequences of a theory ⋮ Computable aspects of the Bachmann–Howard principle ⋮ Derivatives of normal functions in reverse mathematics ⋮ On the structure of the Wadge degrees of bqo-valued Borel functions ⋮ The Reverse Mathematics of wqos and bqos ⋮ From hierarchies to well-foundedness ⋮ HOW STRONG ARE SINGLE FIXED POINTS OF NORMAL FUNCTIONS? ⋮ WELL ORDERING PRINCIPLES AND -STATEMENTS: A PILOT STUDY ⋮ PRIORITY ARGUMENTS VIA TRUE STAGES ⋮ \(\Pi_1^1\)-comprehension as a well-ordering principle ⋮ Proof-theoretic strengths of the well-ordering principles ⋮ Well-ordering Principles, ω-models and $$ \varPi_{1}^{1} $$-comprehension

Cites Work

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• Reverse mathematics and well-ordering principles: a pilot study
• On Fraïssé's conjecture for linear orders of finite Hausdorff rank
• Reverse mathematics and ordinal exponentiation
• The role of parameters in bar rule and bar induction
• Systems of predicative analysis
• The consistency of arithmetics

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