equivalence of forcing notions

Let P and Q be two forcingMathworldPlanetmath notions such that given any genericPlanetmathPlanetmathPlanetmath subset G of P there is a generic subset H of Q with 𝔐[G]=𝔐[H] and vice-versa. Then P and Q are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.

Since if G𝔐[H], τ[G]𝔐 for any P-name τ, it follows that if G𝔐[H] and H𝔐[G] then 𝔐[G]=𝔐[H].

Title equivalence of forcing notions
Canonical name EquivalenceOfForcingNotions
Date of creation 2013-03-22 12:54:24
Last modified on 2013-03-22 12:54:24
Owner Henry (455)
Last modified by Henry (455)
Numerical id 5
Author Henry (455)
Entry type Definition
Classification msc 03E35
Classification msc 03E40
Synonym equivalent
Related topic Forcing
Related topic ProofThatForcingNotionsAreEquivalentToTheirComposition