Lexicographic exponentiation of chains


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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

@article{Holland2005Lexic-16742, title={Lexicographic exponentiation of chains}, year={2005}, doi={10.2178/jsl/1120224719}, 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} }

2005 terms-of-use McCleary, Stephen Kuhlmann, Salma eng McCleary, Stephen Kuhlmann, Salma Holland, Charles W. 2011-11-16T10:03:47Z Publ. in: Journal of Symbolic Logic ; 70 (2005), 2. - pp. 389-409 Lexicographic exponentiation of chains 2011-11-16T10:03:47Z 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:<br /><br />(1) For a countably infinite ordinal α, ℝα * +α≃ℝ α.<br /><br />(2) ℝ ℝ≂ℝ ℚ.<br /><br />(3) For Δ a countable ordinal ≥ 2, Δ ℝ, with its smallest element deleted, is 2-homogeneous. Holland, Charles W.

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