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'''Note on notation.'''  When there is only one sign relation <math>L_J = L(J)</math> associated with a given interpreter <math>J</math>, it is convenient to use the following forms of abbreviation:
 
'''Note on notation.'''  When there is only one sign relation <math>L_J = L(J)</math> associated with a given interpreter <math>J</math>, it is convenient to use the following forms of abbreviation:
   −
:{| cellpadding=4
+
{| align="center" cellspacing="6" width="90%"
| ''J''<sub>''OS''</sub>
+
|
| = || ''Den''(''L''<sub>''J''&nbsp;</sub>)
+
<math>\begin{array}{lclclclcl}
| = || ''Proj''<sub>''OS''&nbsp;</sub>''L''<sub>''J''</sub>
+
J_{OS}
| = || (''L''<sub>''J''&nbsp;</sub>)<sub>''OS''</sub>
+
& = & \operatorname{Den}(L_J)
| = || ''L''(''J'')<sub>''OS''</sub>
+
& = & \operatorname{proj}_{OS} L_J
|-
+
& = & (L_J)_{OS}
| ''J''<sub>''SI''</sub>
+
& = & L(J)_{OS}
| = || ''Con''(''L''<sub>''J''&nbsp;</sub>)
+
\\[6pt]
| = || ''Proj''<sub>''SI''&nbsp;</sub>''L''<sub>''J''</sub>
+
J_{SI}
| = || (''L''<sub>''J''&nbsp;</sub>)<sub>''SI''</sub>
+
& = & \operatorname{Con}(L_J)
| = || ''L''(''J'')<sub>''SI''</sub>
+
& = & \operatorname{proj}_{SI} L_J
|-
+
& = & (L_J)_{SI}
| ''J''<sub>''OI''</sub>
+
& = & L(J)_{SI}
| = || ''Int''(''L''<sub>''J''&nbsp;</sub>)
+
\\[6pt]
| = || ''Proj''<sub>''OI''&nbsp;</sub>''L''<sub>''J''</sub>
+
J_{OI}
| = || (''L''<sub>''J''&nbsp;</sub>)<sub>''OI''</sub>
+
& = & \operatorname{Int}(L_J)
| = || ''L''(''J'')<sub>''OI''</sub>
+
& = & \operatorname{proj}_{OI} L_J
 +
& = & (L_J)_{OI}
 +
& = & L(J)_{OI}
 +
\end{array}</math>
 
|}
 
|}
  
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