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epsilon numbers 1nimbers 1ordinal arithmetic 1quadratically closed fields 1transcendental ordinals 1

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1 paper

math.LO2026

Some quadratically closed fields of nimbers

Lucia Risnoveanu

The paper studies Nim arithmetic on ordinals and identifies the next quadratically closed field ordinals after ε₀, showing that the set {ε_α | α ≤ Ω^{Ω^Ω}} forms this next class.