 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-19/5/i/a/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 19 / 5 / i / a / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-07

The valuation of a forcing name is defined recursively by

val (τ, H) = τ^{H} = {σ^{H} : \exists q \in H ((σ, q) \in τ)} .

(1)

The recursion is on forcing name rank. Only pairs with an active condition in

H

contribute elements, and their first coordinates are evaluated in the same filter. Thus a name is a ground-model set, while its value is a set in the generic extension.

 Read the full article

 New to topics? Read the docs here!