The completeness axiom of Lobachevskian geometry

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8c97ks866

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Attribute Name	Values
Creator	Hartvigson, Zenas Russell
Abstract	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.
Resource Type	Dissertation
Date Available	2010-07-22T15:16:40+00:00
Date Issued	1973-07-25
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	1974
Advisor	Goheen, Harry
Academic Affiliation	Mathematics
Non-Academic Affiliation	Oregon State University. Graduate School
Subject	Geometry, Non-Euclidean
权利声明	Copyright Not Evaluated
Publisher	Oregon State University
Language	English [eng]
Digitization Specifications	File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
Replaces	http://hdl.handle.net/1957/17015

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