Abstract
When we iterate we are faced with the problem of obtaining for the iteration the good properties of the single steps of iteation. Usually the worst possible vice of a forcing notion is that it collapses ℵ 1. The virtue of not collapsing ℵ 1 is not inherited by the iteration from its single components. As we saw, the virtue of the c.c.c. is inherited by the FS iteration from its components. However the c.c.c. is too strong a requirement. We shall look for a weaker requirement which is more naturally connected to the property of not collapsing ℵ l, and which is inherited by iterations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shelah, S. (1982). Proper Forcing. In: Proper Forcing. Lecture Notes in Mathematics, vol 940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21543-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-21543-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11593-9
Online ISBN: 978-3-662-21543-2
eBook Packages: Springer Book Archive