Lexicographic exponentiation of chains
Holland, W. C. ; Kuhlmann, S. ; McCleary, S. H.
J. Symbolic Logic, Tome 70 (2005) no. 1, p. 389-409 / Harvested from Project Euclid
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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.
Publié le : 2005-06-14
Classification:  06A05,  03C60 
@article{1120224719,
     author = {Holland, W. C. and Kuhlmann, S. and McCleary, S. H.},
     title = {Lexicographic exponentiation of chains},
     journal = {J. Symbolic Logic},
     volume = {70},
     number = {1},
     year = {2005},
     pages = { 389-409},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120224719}
}

Holland, W. C.; Kuhlmann, S.; McCleary, S. H. Lexicographic exponentiation of chains. J. Symbolic Logic, Tome 70 (2005) no. 1, pp.  389-409. http://gdmltest.u-ga.fr/item/1120224719/