TL;DR
This paper generalizes Conway's On_2 to construct fields of characteristic p for any prime p, defining minimal operations to turn ordinals into such fields and analyzing their structure.
Contribution
It introduces minimal definitions of addition and multiplication to form fields of characteristic p from ordinals, extending Conway's On_2 construction.
Findings
Constructed fields of characteristic p from ordinals
Defined minimal operations for field structure
Analyzed the algebraic structure of On_p
Abstract
Generalizing John Conway's construction of the Field On_2, we give the "minimal" definitions of addition and multiplication that turn the ordinals into a Field of characteristic p, for any prime p. We then analyze the structure of the resulting Field, which we will call On_p.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Computability, Logic, AI Algorithms · History and Theory of Mathematics