Transfinite induction within Peano arithmetic

DOI10.1016/0168-0072(95)00029-GzbMath0858.03056OpenAlexW2025460262MaRDI QIDQ1919522

Richard Sommer

Publication date: 19 March 1997

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(95)00029-g

zbMATH Keywords

upper boundstransfinite inductionprovably recursive functions

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30)

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A MATHEMATICAL COMMITMENT WITHOUT COMPUTATIONAL STRENGTH ⋮ More on lower bounds for partitioning \(\alpha\)-large sets ⋮ Transfinite induction within Peano arithmetic ⋮ Slow reflection ⋮ Short proofs for slow consistency ⋮ What is effective transfinite recursion in reverse mathematics? ⋮ PREDICATIVE COLLAPSING PRINCIPLES ⋮ Weak and strong versions of effective transfinite recursion ⋮ Set-theoretic reflection is equivalent to induction over well-founded classes ⋮ A Model-Theoretic Approach to Ordinal Analysis ⋮ Parameter free induction and provably total computable functions ⋮ Proof Theoretic Analysis by Iterated Reflection ⋮ Proof lengths for instances of the Paris-Harrington principle ⋮ Some results on cut-elimination, provable well-orderings, induction and reflection ⋮ Partitioning 𝛼–large sets: Some lower bounds ⋮ ON THE INVARIANCE OF GÖDEL’S SECOND THEOREM WITH REGARD TO NUMBERINGS ⋮ Variations on a theme by Weiermann

Cites Work

• Rapidly growing Ramsey functions
• Ordinal complexity of recursive definitions
• Transfinite induction within Peano arithmetic
• Exact estimates of the provability of transfinite induction in the initial segments of arithmetic
• Theory of Formal Systems. (AM-47)
• A classification of the ordinal recursive functions
• Transfinite recursive progressions of axiomatic theories
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