Forcing (computability): Difference between revisions

Revision as of 12:26, 4 February 2012

Revision as of 08:08, 9 July 2012

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;Ultrafilter : A maximal filter, i.e., <math>F</math> is an ultrafilter if <math>F</math> is a filter and there is no filter <math>F'</math> properly containing <math>F</math>

; Cohen forcing: The notion of forcing <math>C</math> where conditions are elements of <math>(2^{<\omega}</math> and <math>(\tau \succ_C \sigma \iff \sigma \supset \tau</math>)

Note that for Cohen forcing <math>\succ_{C}</math> is the '''reverse''' of the containment relation. This leads to an unfortunate notational confusion where some recursion theorists reverse the direction of the forcing partial order (exchanging <math>\succ_P</math> with <math>\prec_P</math> which is more natural for Cohen forcing but is at odds with the notation used in set theory.