Let be a forcing notion.
For , is the set of all functions such that and for any , is a -name for a member of . Order by the rule iff and for any , . (Translated, this means that any generic subset including restricted to forces that , an element of , be less than .)
For , is a forcing notion in (so is a forcing notion).
Then the sequence is an iterated forcing.
If is restricted to finite functions that it is called a finite support iterated forcing (FS), if is restricted to countable functions, it is called a countable support iterated function (CS), and in general if each function in each has size less than then it is a -support iterated forcing.
Typically we construct the sequence of ’s by induction, using a function such that .
|Date of creation||2013-03-22 12:54:47|
|Last modified on||2013-03-22 12:54:47|
|Last modified by||Henry (455)|
|Defines||finite support iterated forcing|
|Defines||countable support iterated forcing|
|Defines||support iterated forcing|