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| ===Definition 9=== | | ===Definition 9=== |
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− | <pre>
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− | Definition 9
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− | If R c OxSxI,
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− | then the following are identical subsets of IxS:
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− | D9a. RIS
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− | D9b. RSI^
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− | D9c. ConR^
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− | D9d. Con(R)^
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− | D9e. PrIS(R)
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− | D9f. Conv(Con(R))
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− | D9g. {<i, s> C IxS : <o, s, i> C R for some o C O}
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− | </pre>
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| <br> | | <br> |
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| |- style="height:40px; text-align:center" | | |- style="height:40px; text-align:center" |
| | width="80%" | | | | width="80%" | |
− | | width="20%" | <math>\operatorname{Definition~8}</math> | + | | width="20%" | <math>\operatorname{Definition~9}</math> |
| |} | | |} |
| |- | | |- |
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| | <math>\text{then}\!</math> | | | <math>\text{then}\!</math> |
− | | <math>\text{the following are identical subsets of}~ S \times I \, :</math> | + | | <math>\text{the following are identical subsets of}~ I \times S \, :</math> |
| |} | | |} |
| |- | | |- |
| | | | | |
| {| align="center" cellpadding="0" cellspacing="0" width="100%" | | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
− | |- style="height:40px" | + | |- style="height:50px" |
| | width="2%" style="border-top:1px solid black" | | | | width="2%" style="border-top:1px solid black" | |
− | | width="18%" style="border-top:1px solid black" | <math>\operatorname{D8a.}</math> | + | | width="18%" style="border-top:1px solid black" | <math>\operatorname{D9a.}</math> |
− | | width="80%" style="border-top:1px solid black" | <math>L_{SI}\!</math> | + | | width="80%" style="border-top:1px solid black" | <math>L_{IS}\!</math> |
− | |- style="height:40px" | + | |- style="height:50px" |
| + | | |
| + | | <math>\operatorname{D9b.}</math> |
| + | | <math>\overset{\smile}{L_{SI}}</math> |
| + | |- style="height:50px" |
| + | | |
| + | | <math>\operatorname{D9c.}</math> |
| + | | <math>\overset{\smile}{\operatorname{Con}^L}</math> |
| + | |- style="height:50px" |
| | | | | |
− | | <math>\operatorname{D8b.}</math> | + | | <math>\operatorname{D9d.}</math> |
− | | <math>\operatorname{Con}^L</math> | + | | <math>\overset{\smile}{\operatorname{Con}(L)}</math> |
− | |- style="height:40px" | + | |- style="height:50px" |
| | | | | |
− | | <math>\operatorname{D8c.}</math> | + | | <math>\operatorname{D9e.}</math> |
− | | <math>\operatorname{Con}(L)</math> | + | | <math>\operatorname{proj}_{IS}(L)</math> |
− | |- style="height:40px" | + | |- style="height:50px" |
| | | | | |
− | | <math>\operatorname{D8d.}</math> | + | | <math>\operatorname{D9f.}</math> |
− | | <math>\operatorname{proj}_{SI}(L)</math> | + | | <math>\operatorname{Conv}(\operatorname{Con}(L))</math> |
− | |- style="height:40px" | + | |- style="height:50px" |
| | | | | |
− | | <math>\operatorname{D8e.}</math> | + | | <math>\operatorname{D9g.}</math> |
− | | <math>\{ (s, i) \in S \times I ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math> | + | | <math>\{ (i, s) \in I \times S ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math> |
| |} | | |} |
| |} | | |} |