Lexicographic exponentiation of chains

Holland, Charles W.; Kuhlmann, Salma; McCleary, Stephen

Lexicographic exponentiation of chains

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Date

2005

Authors

Holland, Charles W.

Kuhlmann, Salma

McCleary, Stephen

Publication type

Journal article

Published in

The Journal of Symbolic Logic ; 70 (2005), 02. - pp. 389-409. - ISSN 0022-4812

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 * +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.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

HOLLAND, Charles W., Salma KUHLMANN, Stephen MCCLEARY, 2005. Lexicographic exponentiation of chains. In: The Journal of Symbolic Logic. 70(02), pp. 389-409. ISSN 0022-4812. Available under: doi: 10.2178/jsl/1120224719

BibTex

@article{Holland2005Lexic-16742,
  year={2005},
  doi={10.2178/jsl/1120224719},
  title={Lexicographic exponentiation of chains},
  number={02},
  volume={70},
  issn={0022-4812},
  journal={The Journal of Symbolic Logic},
  pages={389--409},
  author={Holland, Charles W. and Kuhlmann, Salma and McCleary, Stephen}
}

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