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Lexicographic exponentiation of chains
Published online by Cambridge University Press: 12 March 2014
Abstract
The lexicographic power ΔΓ of chains Δ and Γ is, roughly, the Cartesian power ΠγЄΓΔ totally ordered lexicographically from the left. Here the focus is on certain powers in which either Δ = ℝ or ℚ = ℝ, with emphasis on when two such powers are isomorphic and on when ΔΓ is 2-homogeneous. The main results are:
(1) For a countably infinite ordinal
(2) ℝℝ ≄ ℝℚ.
(3) For Δ a countable ordinal ≥ 2, Δℝ with its smallest element deleted, is 2-homogeneous.
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- Copyright © Association for Symbolic Logic 2005
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