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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 05:38, 9 February 2009

44 bytes added , 05:38, 9 February 2009

→‎Definition 9

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===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>~~

<br>

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|- style="height:40px; text-align:center"

| width="80%" |  

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| width="20%" | <math>\operatorname{Definition~8}</math>

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| width="20%" | <math>\operatorname{Definition~9}</math>

|}

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|  

| <math>\text{then}\!</math>

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| <math>\text{the following are identical subsets of}~ S \times I \, :</math>

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| <math>\text{the following are identical subsets of}~ I \times S \, :</math>

|}

|-

|

{| align="center" cellpadding="0" cellspacing="0" width="100%"

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|- style="height:~~40px~~"

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|- style="height:50px"

| width="2%" style="border-top:1px solid black" |  

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| width="18%" style="border-top:1px solid black" | <math>\operatorname{~~D8a~~.}</math>

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| width="18%" style="border-top:1px solid black" | <math>\operatorname{D9a.}</math>

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| width="80%" style="border-top:1px solid black" | <math>L_{SI}\!</math>

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| width="80%" style="border-top:1px solid black" | <math>L_{IS}\!</math>

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|- style="height:~~40px~~"

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|- style="height:50px"

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|  

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| <math>\operatorname{D9b.}</math>

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| <math>\overset{\smile}{L_{SI}}</math>

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|- style="height:50px"

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|  

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| <math>\operatorname{D9c.}</math>

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| <math>\overset{\smile}{\operatorname{Con}^L}</math>

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|- style="height:50px"

|  

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| <math>\operatorname{~~D8b~~.}</math>

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| <math>\operatorname{D9d.}</math>

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| <math>\operatorname{Con}^L</math>

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| <math>\overset{\smile}{\operatorname{Con}(L)}</math>

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|- style="height:~~40px~~"

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|- style="height:50px"

|  

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| <math>\operatorname{~~D8c~~.}</math>

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| <math>\operatorname{D9e.}</math>

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| <math>\operatorname{~~Con~~}(L)</math>

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| <math>\operatorname{proj}_{IS}(L)</math>

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|- style="height:~~40px~~"

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|- style="height:50px"

|  

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| <math>\operatorname{~~D8d~~.}</math>

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| <math>\operatorname{D9f.}</math>

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| <math>\operatorname{~~proj~~}_{SI}(L)</math>

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| <math>\operatorname{Conv}(\operatorname{Con}(L))</math>

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|- style="height:~~40px~~"

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|- style="height:50px"

|  

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| <math>\operatorname{~~D8e~~.}</math>

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| <math>\operatorname{D9g.}</math>

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| <math>\{ (s~~, i~~) \in S \times I ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math>

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| <math>\{ (i, s) \in I \times S ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math>

|}

Jon Awbrey

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