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.
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Explicit formulas and asymptotic bounds are derived for the counts of countable homogeneous colored linear orderings in k colors and C_{n,m}-homogeneous linear orderings by mapping them to finite combinatorial objects.
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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.
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Enumerative Combinatorics of Homogeneous Linear Orderings
Explicit formulas and asymptotic bounds are derived for the counts of countable homogeneous colored linear orderings in k colors and C_{n,m}-homogeneous linear orderings by mapping them to finite combinatorial objects.