TL;DR
This paper introduces a new framework for ordinal notation systems, providing simple yet powerful systems with examples, some of which may surpass traditional set-theoretic strength, and proves well-foundedness for certain variants.
Contribution
It presents a novel framework for ordinal notation, introduces strong systems with examples, and establishes well-foundedness for some conjectural and weakened versions.
Findings
Systems with conjectured strength beyond second order arithmetic
Proof of well-foundedness for some weakened systems
Examples of ordinals within the new notation framework
Abstract
We introduce a framework for ordinal notation systems, present a family of strong yet simple systems, and give many examples of ordinals in these systems. While much of the material is conjectural, we include systems with conjectured strength beyond second order arithmetic (and plausibly beyond ZFC), and prove well-foundedness for some weakened versions.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Advanced Topology and Set Theory