Classifies sp-homogeneous linear orderings with successor/predecessor, proves relative Δ4 categoricity for all and determines the Δ3 ones, with Π5^0-completeness for the sp-homogeneous set and Σ6^0-completeness for the weak version.
Montalbán,Counting the back-and-forth types, Journal of Logic and Computation22(2012), 857–876
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sp-Homogeneous Linear Orderings
Classifies sp-homogeneous linear orderings with successor/predecessor, proves relative Δ4 categoricity for all and determines the Δ3 ones, with Π5^0-completeness for the sp-homogeneous set and Σ6^0-completeness for the weak version.