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June 2005 Lexicographic exponentiation of chains
W. C. Holland, S. Kuhlmann, S. H. McCleary
J. Symbolic Logic 70(2): 389-409 (June 2005). DOI: 10.2178/jsl/1120224719

Abstract

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 *≃ℝ α.

(2) ℝ ≂ℝ .

(3) For Δ a countable ordinal ≥ 2, Δ , with its smallest element deleted, is 2-homogeneous.

Citation

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W. C. Holland. S. Kuhlmann. S. H. McCleary. "Lexicographic exponentiation of chains." J. Symbolic Logic 70 (2) 389 - 409, June 2005. https://doi.org/10.2178/jsl/1120224719

Information

Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1106.03032
MathSciNet: MR2140037
Digital Object Identifier: 10.2178/jsl/1120224719

Subjects:
Primary: 06A05
Secondary: 03C60

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 2 • June 2005
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