Complexity and (un)decidability of fragments of 〈 ω^ω^λ; ×〉

03/04/2018

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by   Alexis Bès, et al.

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We specify the frontier of decidability for fragments of the first-order theory of ordinal multiplication. We give a NEXPTIME lower bound for the complexity of the existential fragment of 〈ω^ω^λ; ×, ω, ω+1, ω^2+1 〉 for every ordinal λ. Moreover, we prove (by reduction from Hilbert Tenth Problem) that the ∃^*∀^6-fragment of 〈ω^ω^λ; ×〉 is undecidable for every ordinal λ.