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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'' </sub>)
| + | <math>\begin{array}{lclclclcl} |
− | | = || ''Proj''<sub>''OS'' </sub>''L''<sub>''J''</sub>
| + | J_{OS} |
− | | = || (''L''<sub>''J'' </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'' </sub>)
| + | \\[6pt] |
− | | = || ''Proj''<sub>''SI'' </sub>''L''<sub>''J''</sub>
| + | J_{SI} |
− | | = || (''L''<sub>''J'' </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'' </sub>)
| + | \\[6pt] |
− | | = || ''Proj''<sub>''OI'' </sub>''L''<sub>''J''</sub>
| + | J_{OI} |
− | | = || (''L''<sub>''J'' </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> |
| |} | | |} |
| | | |