International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 2, Pages 63-82
doi:10.1155/S016117120102018X

Iteration of λ-complete forcing notions not collapsing λ+

Andrzej Rosłanowski1 and Saharon Shelah2,3

 1Department of Mathematics, University of Nebraska at Omaha, Omaha 68182-0243, NE, USA
2Department of Mathematics, Rutgers University, New Brunswick 08854, NJ, USA
3Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Received 25 February 2001; Revised 6 August 2001

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.