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Revision as of 04:48, 9 February 2009
, 04:48, 9 February 2009→Derived Equivalence Relations: format definition box
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
Definition 8
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
If R c OxSxI,
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then the following are identical subsets of SxI:
| width="20%" | <math>\operatorname{Definition~8}</math>
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D8a. RSI
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D8b. ConR
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D8c. Con(R)
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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
D8d. PrSI(R)
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
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D8e. {<s, i> C SxI : <o, s, i> C R for some o C O}
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| <math>\text{then}\!</math>
| <math>\text{the following are identical subsets of}~ S \times I \, :</math>
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D8a.}</math>
| width="80%" style="border-top:1px solid black" | <math>L_{SI}\!</math>
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| <math>\operatorname{D8b.}</math>
| <math>\operatorname{Con}^L</math>
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| <math>\operatorname{D8c.}</math>
| <math>\operatorname{Con}(L)</math>
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| <math>\operatorname{D8d.}</math>
| <math>\operatorname{proj}_{SI}(L)</math>
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| <math>\operatorname{D8e.}</math>
| <math>\{ (s, i) \in S \times I ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math>
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