Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've recently read a paper about sheaf forcing in which a sheaf of cumulative hierarchies was defined (defintion 5.3 on page 30). The same object is described in this English paper (defintion 3.1 on page 16). There was however no mention of the idea behind it's construction.

I would like to know more about this cumulative hierarchy of variable sets, but I don't quite know where to look. I suspect a more general version of the object can be found in Mac Lane and Moerdijk's "Sheafs in Geometry and Logic". Is this true and are there other treatments of this subject?

share|cite|improve this question
Ick. This looks like a terrifying hybrid of the cumulative hierarchy of set theory and sheaf theory. It is indeed based on forcing techniques (more precisely, boolean-valued models) from set theory, but you won't find it in Mac Lane and Moerdijk's book. – Zhen Lin Dec 21 '12 at 1:36

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.