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Lexicographic exponentiation of chains

Published online by Cambridge University Press:  12 March 2014

W. C. Holland ,
S. Kuhlmann  and
S. H. McCleary
W. C. Holland
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green. Ohio 43403., USA, E-mail: [email protected] Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OHIO 43403., USA
S. Kuhlmann
Affiliation:
Research Unit Algebra and Logic, University of Saskatchewan, Mclean Hall, 106 Wiggins Road, Saskatoon. SK S7N 5E6., Canada, E-mail: [email protected] Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OHIO 43403., USA
S. H. McCleary
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OHIO 43403., USA 7180 Las Vistas Las Cruces, New Mexico 88005., USA, E-mail: [email protected]
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 389 - 409
Copyright
Copyright © Association for Symbolic Logic 2005

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References

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