§ Forcing machinery

§ Ideal of a post

§ Maximal ideal

§ Density in a poset

§ Generic Ideals

§ Proof: Generic ideal always exists

§ Separative poset

§ Generic ideal of separative poset is not in the model

§ Definition of forcing

§ Fundamental theorem of forcing

§ Architecture of FTF

§ Net to capture generic ideal

 
 
a   r
 \ / \
  p   d  e
   \ /   |
    c----*

§ Proof of net lemma

§ Simpler proof of net lemma (Unverified)

§ Intuition for Net definition

§ Names and name creation

§ Forcing equality

§ Step 1: Defining the forcing tuple set Fx=yF^{x=y}.

§ Step 2: defining the net

§ Step 4: The equivalence of net, modality, relativized inclusion:

Therefore, all these conditions are equivalent.

§