This question is from Kunen's set theory book.

My questions are:

  • What is the definition of isomorphism between forcing notions?

  • When do we say that two forcing notions $\mathbb{P},\mathbb{Q}$ are equivalent?

  • Are these two (i.e. Isomorphism and equivalence) between forcing notions same or there are equivalent forcing notions that are not isomorphic?

  • How to find out that two forcing notions are isomorphic?


closed as off-topic by user223391, Harish Chandra Rajpoot, Em., colormegone, Claude Leibovici Jan 14 '16 at 8:10

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  • $\begingroup$ Please provide a bit more context to this question. For example, have you seen these terms defined anywhere? A common reference is a helpful starting point $\endgroup$ – Omnomnomnom Jan 14 '16 at 6:25
  • $\begingroup$ @Omnomnomnom I have seen these terms being used here in this site in several occasions (I can't remember where exactly). In those posts people say this or that forcing notions are "equivalent" or "isomorphic" and it seems that they assumed these notions are clear to the audience. I don't know if these two are same. $\endgroup$ – Curious Guy Jan 14 '16 at 6:31
  • $\begingroup$ @Omnomnomnom I added a reference for my question. $\endgroup$ – Curious Guy Jan 14 '16 at 12:14
  • 2
    $\begingroup$ Two forcing notions are equivalent iff their Boolean completions are isomorphic. All these terms are explained in the book you mentioned. $\endgroup$ – Andrés E. Caicedo Jan 14 '16 at 14:42
  • $\begingroup$ Adding to Andrés' comment: In the 2013 edition of Kunen's Set Theory, this is discussed in IV.4 (Embeddings of Posets). $\endgroup$ – Stefan Mesken Jan 14 '16 at 18:48