Recursive Analogues of Shrewdness and Subtlety, with Applications to Fine Structure

Jayde Sylvie Massmann

Recursive Analogues of Shrewdness and Subtlety, with Applications to Fine Structure

Logic 2024-07-09 v3

Authors: Jayde Sylvie Massmann

Abstract

We share both recent and older, well-known results regarding the notions of stable ordinals and shrewd cardinals. We then argue that $\Sigma_2$ -nonprojectible ordinals may be considered as recursive analogues to subtle cardinals, a highly combinatorial type of cardinal related to Jensen's fine structure, due to the latter possessing a characterisation in terms of shrewdnesss.

Keywords

stable ordinals shrewd cardinals subtle cardinals Σ₂-nonprojectible ordinals fine structure recursive analogues

Cite

@article{arxiv.2312.15818,
  title  = {Recursive Analogues of Shrewdness and Subtlety, with Applications to Fine Structure},
  author = {Jayde Sylvie Massmann},
  journal= {arXiv preprint arXiv:2312.15818},
  year   = {2024}
}

Comments

11 pages, no figures, preprint, independent research. Updated twice: 1st time it was a large modification as I realized that the main theorem was false. The 2nd time was adding a single sentence of credit as said credit was due

Recursive Analogues of Shrewdness and Subtlety, with Applications to Fine Structure

Abstract

Keywords

Cite

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