The completeness axiom of Lobachevskian geometry Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8c97ks866

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  • This paper gives a proof that the Completeness Axiom of Lobachevskian geometry -- as formulated in the second English translation of David Hilbert's Foundations of Geometry (tenth German edition)--is a theorem in the three dimensional Poincare model. An explicit canonical isomorphism between all models of Lobachevskian space is given. This, together with the work of William Lee Zell (A Model of Non-Euclidean Geometry in Three Dimensions, Master's Thesis, Oregon State University, 1967) and Robert W. Eschrich (A Model of Non-Euclidean Geometry in Three Dimensions, II, Master's Thesis, Oregon State University, 1968), establishes that the three dimensional Poincar4 model is a model of Lobachevskian geometry based upon Hilbert's axioms.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-07-22T15:16:40Z (GMT) No. of bitstreams: 1 RedactedHartvigsonZenasRussell1974.pdf: 2369543 bytes, checksum: 3dc328dba004864788f7532862e602d6 (MD5)
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-07-22T15:14:58Z (GMT) No. of bitstreams: 1 RedactedHartvigsonZenasRussell1974.pdf: 2369543 bytes, checksum: 3dc328dba004864788f7532862e602d6 (MD5)
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