ON THE HIERARCHY OF NATURAL THEORIES

Abstract It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of “natural,” it is unclear how to study this phenomenon mathematically. We will discuss the significance of this problem and survey some strategies that have recently been developed for addressing it. These strategies emphasize the role of reflection principles and ordinal analysis and draw on analogies with research in recursion theory.

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Publication Details

Journal
Bulletin of Symbolic Logic
Published
2025-12-04
DOI
https://doi.org/10.1017/bsl.2025.10137
Citations
1
Primary Topic
Computability, Logic, AI Algorithms
Type
article
Field-Weighted Citation Impact
1.50
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article

ON THE HIERARCHY OF NATURAL THEORIES

James P. Walsh
1 citations
Bulletin of Symbolic Logic
Computability, Logic, AI Algorithms
1.50
article

ON THE HIERARCHY OF NATURAL THEORIES

James P. Walsh
article en
1 citations

Abstract

Abstract It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of “natural,” it is unclear how to study this phenomenon mathematically. We will discuss the significance of this problem and survey some strategies that have recently been developed for addressing it. These strategies emphasize the role of reflection principles and ordinal analysis and draw on analogies with research in recursion theory.

Bulletin of Symbolic LogicVol. 32(1)
New York University (US)
Openalex Percentile: Top 12%
Computability, Logic, AI Algorithms
1.50
DOIOpen Access PDFOpenAlex
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ON THE HIERARCHY OF NATURAL THEORIES — James P. Walsh · Bulletin of Symbolic Logic (2025) | TGRS Research Map | TGRS