The lexicographic power Δ Γ of chains Δ and Γ is, roughly, the Cartesian power ∏γ ∈ ΓΔ, totally ordered lexicographically from the left. Here the focus is on certain powers in which either Δ = ℝ or Γ = ℝ, with emphasis on when two such powers are isomorphic and on when Δ Γ is 2-homogeneous. The main results are:
(1) For a countably infinite ordinal α, ℝα * +α≃ℝ α.
(2) ℝ ℝ≂ℝ ℚ.
(3) For Δ a countable ordinal ≥ 2, Δ ℝ, with its smallest element deleted, is 2-homogeneous.
"Lexicographic exponentiation of chains." J. Symbolic Logic 70 (2) 389 - 409, June 2005. https://doi.org/10.2178/jsl/1120224719