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International Journal of Mathematics and Mathematical Sciences
Volume 28, Issue 2, Pages 63-82
http://dx.doi.org/10.1155/S016117120102018X

Iteration of λ-complete forcing notions not collapsing λ+

1Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA
2Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA
3Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Received 25 February 2001; Revised 6 August 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We look for a parallel to the notion of “proper forcing” among λ-complete forcing notions not collapsing λ+. We suggest such a definition and prove that it is preserved by suitable iterations.