forcing relation

If 𝔐 is a transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath model of set theoryMathworldPlanetmath and P is a partial orderMathworldPlanetmath then we can define a forcing relation:


(p forces ϕ(τ1,,τn))

for any pP, where τ1,,τn are P- names.

Specifically, the relationMathworldPlanetmathPlanetmath holds if for every generic filter G over P which contains p,


That is, p forces ϕ if every of 𝔐 by a generic filter over P containing p makes ϕ true.

If pPϕ holds for every pP then we can write Pϕ to mean that for any generic GP, 𝔐[G]ϕ.

Title forcing relation
Canonical name ForcingRelation
Date of creation 2013-03-22 12:53:28
Last modified on 2013-03-22 12:53:28
Owner Henry (455)
Last modified by Henry (455)
Numerical id 5
Author Henry (455)
Entry type Definition
Classification msc 03E35
Classification msc 03E40
Related topic ForcingMathworldPlanetmath
Defines forcing relation
Defines forces