Abstract
Neither the Plane-Separation Postulate (PSP) nor Pasch’s Postulate (PASCH) have been formally introduced into our theory. Neither can be a theorem for Σ at this time. Which one shall we take as a new axiom? It turns out not to make any difference! We shall first show that PASCH implies PSP. The proof is quite long and may even be omitted without loss of continuity because we shall actually take PSP as our third axiom. Then PASCH later turns up as a theorem.
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© 1975 Springer-Verlag New York, Inc.
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Martin, G.E. (1975). Pasch’s Postulate and Plane Separation Postulate. In: The Foundations of Geometry and the Non-Euclidean Plane. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5725-7_12
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DOI: https://doi.org/10.1007/978-1-4612-5725-7_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5727-1
Online ISBN: 978-1-4612-5725-7
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