Introducing the hardline in proof theory
Toshiyasu Arai
TL;DR
This paper explores proof theory related to theories of ordinals with numerous stable ordinals below them, aiming to deepen understanding of their foundational properties.
Contribution
It introduces new ideas in proof theory specifically focused on theories involving complex ordinal structures with many stable ordinals.
Findings
Develops a framework for analyzing theories of ordinals with stable ordinals
Provides insights into the structure of proof-theoretic strength for such theories
Suggests potential applications in foundational mathematics and ordinal analysis
Abstract
In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Logic, Reasoning, and Knowledge · Advanced Algebra and Logic