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Forms of the Pasch axiom in ordered geometry
Author(s) -
Pambuccian Victor
Publication year - 2010
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200810032
Subject(s) - axiom , mathematics , geometry , mathematical economics , pure mathematics
We prove that, in the framework of ordered geometry, the inner form of the Pasch axiom ( IP ) does not imply its outer form ( OP ). We also show that OP can be properly split into IP and the weak Pasch axiom ( WP ) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)