Another splitting of the Pasch axiom (Q545487)
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scientific article; zbMATH DE number 5911444
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Another splitting of the Pasch axiom |
scientific article; zbMATH DE number 5911444 |
Statements
Another splitting of the Pasch axiom (English)
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22 June 2011
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The author investigates ordered planar domains, which are axiomatized in terms of points and a ternary betweenness relation. In this setting, the inner and the outer form of the Pasch axiom are not equivalent. The author shows that the full Pasch axiom is equivalent to its inner form together with a statement on the intersection of segments involving five variables.
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Pasch axiom
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inner and outer form of Pasch axiom
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ordered planar domain
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splitting an axiom
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