Nonproper Products
Andrzej Roslanowski, Saharon Shelah, Otmar Spinas
TL;DR
This paper demonstrates that the product of two properly defined creature forcings can fail to be proper, and introduces a new condition to ensure properness in certain forcings with norms.
Contribution
It reveals that proper creature forcings can produce nonproper products and proposes a new condition to guarantee properness in forcings with norms.
Findings
Existence of proper creature forcings with nonproper products
Introduction of a new properness condition for forcings with norms
Insights into the behavior of product forcings in set theory
Abstract
We show that there exist two proper creature forcings having a simple (Borel) definition, whose product is not proper. We also give a new condition ensuring properness of some forcings with norms.
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