Higher Classes of Ordinals induced by <₁

2013/09/23 by Parménides García Cornejo, Cornejo, Parménides García
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1309.5996

openalex publication_date 2013/09/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this article we want to see that it is possible to iterate and generalize\nthe notions presented in "Carlson's &lt;₁-relation on the class of epsilon\nnumbers" such that we can obtain the higher or thinner classes of ordinals\ninduced by the &lt;₁-relation as solutions of conditions. Indeed, these results\nare so general that in a future article we will be able to characterize the\nordinal |Pi₁¹ - CA₀ | as the smallest ordinal of the thinnest class induced\nby &lt;₁.\n

Related

• The Theory of Sets of Ordinals
• Ordinal Notation
• Lectures on Ordinal Analysis
• Higher arithmetic on the ordinals
• Ordinal Recursion Theory