\(\Pi_1^1\)-comprehension as a well-ordering principle

DOI10.1016/j.aim.2019.106767zbMath1441.03012arXiv1809.06759OpenAlexW2890902398MaRDI QIDQ2274030

Anton Freund

Publication date: 19 September 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.06759

zbMATH Keywords

ATRreverse mathematicsordinal analysisadmissible setswell-ordering principlesdilators\(\Pi_1^1\)-CA\(\Pi_1^1\)-comprehension

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) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

Related Items

Minimal bad sequences are necessary for a uniform Kruskal theorem, Well-Ordering Principles in Proof Theory and Reverse Mathematics, Well ordering principles for iterated \(\Pi^1_1\)-comprehension, PREDICATIVE COLLAPSING PRINCIPLES, Bachmann-Howard derivatives, Functorial Fast-Growing Hierarchies, The Π21$\Pi ^1_2$ consequences of a theory, Set-theoretic reflection is equivalent to induction over well-founded classes, Computable aspects of the Bachmann–Howard principle, Derivatives of normal functions in reverse mathematics, HOW STRONG ARE SINGLE FIXED POINTS OF NORMAL FUNCTIONS?, WELL ORDERING PRINCIPLES AND -STATEMENTS: A PILOT STUDY, A categorical construction of Bachmann–Howard fixed points, Patterns of resemblance and Bachmann-Howard fixed points, From Kruskal’s theorem to Friedman’s gap condition

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