Can a small forcing create Kurepa trees?
Abstract
In the paper we probe the possibilities of creating a Kurepa tree in a generic extension of a model of CH plus no Kurepa trees by an omega_1preserving forcing notion of size at most omega_1. In the first section we show that in the Levy model obtained by collapsing all cardinals between omega_1 and a strongly inaccessible cardinal by forcing with a countable support Levy collapsing order many omega_1preserving forcing notions of size at most omega_1 including all omegaproper forcing notions and some proper but not omegaproper forcing notions of size at most omega_1 do not create Kurepa trees. In the second section we construct a model of CH plus no Kurepa trees, in which there is an omegadistributive Aronszajn tree such that forcing with that Aronszajn tree does create a Kurepa tree in the generic extension. At the end of the paper we ask three questions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1995
 arXiv:
 arXiv:math/9504220
 Bibcode:
 1995math......4220J
 Keywords:

 Mathematics  Logic
 EPrint:
 Ann. Pure Appl. Logic 85 (1997), 4768