From hierarchies to well-foundedness

DOI10.1007/s00153-014-0392-9zbMath1338.03011OpenAlexW2037274661MaRDI QIDQ481873

Dandolo Flumini, Kentaro Sato

Publication date: 15 December 2014

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

Full work available at URL: https://hdl.handle.net/11475/15846

zbMATH Keywords

intuitionistic logicsecond-order arithmeticwell-foundednesspseudohierarchysecond-order set theorytransfinite recursion

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Nonclassical and second-order set theories (03E70) Second- and higher-order arithmetic and fragments (03F35) Hierarchies of computability and definability (03D55) Abstract and axiomatic computability and recursion theory (03D75)

Related Items

Reflection algebras and conservation results for theories of iterated truth, RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES, A NOTE ON PREDICATIVE ORDINAL ANALYSIS I: ITERATED COMPREHENSION AND TRANSFINITE INDUCTION, Full and hat inductive definitions are equivalent in NBG, Elementary inductive dichotomy: separation of open and clopen determinacies with infinite alternatives, Truth, disjunction, and induction, A new model construction by making a detour via intuitionistic theories. III: Ultrafinitistic proofs of conservations of \(\Sigma_1^1\) collection

Cites Work

• RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES
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• Descending sequences of degrees
• Intuitionistic Fixed Point Theories for Strictly Positive Operators
• Set Theory
• Systems of predicative analysis