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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 04:42, 9 February 2009

89 bytes added , 04:42, 9 February 2009

→‎Definition 8

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===Definition 8===

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~~<pre>~~

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~~Definition 8~~

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~~If R c OxSxI,~~

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~~then the following are identical subsets of SxI:~~

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~~D8a. RSI~~

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~~D8b. ConR~~

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~~D8c. Con(R)~~

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~~D8d. PrSI(R)~~

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~~D8e. {<s, i> C SxI : <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~4}</math>

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

|}

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

| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>

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| width="80%" style="border-top:1px solid black" | <math>Q ~\subseteq~ X</math>

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| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>

|- style="height:40px"

|  

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

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| <math>\text{the following are identical subsets of}~ X \times \~~underline\mathbb{B}~~:</math>

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

|}

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|- style="height:40px"

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

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| width="18%" style="border-top:1px solid black" | <math>\operatorname{~~D4a~~.}</math>

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

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| width="80%" style="border-top:1px solid black" | <math>\~~upharpoonleft Q~~ \~~upharpoonright~~</math>

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

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|- style="height:40px"

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|  

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

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

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|- style="height:40px"

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|  

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

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

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|- style="height:40px"

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|  

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

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

|- style="height:40px"

|  

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| <math>\operatorname{~~D4b~~.}</math>

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

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| <math>\{ (x, y) \in X \times \~~underline~~\~~mathbb~~{B} ~~~:~ y ~=~ \downharpoonleft x~~ \in Q \~~downharpoonright~~</math>

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

|}

Jon Awbrey

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