# Sh:563

• Jin, R., & Shelah, S. (1997). Can a small forcing create Kurepa trees. Ann. Pure Appl. Logic, 85(1), 47–68.
• 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_1-preserving 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_1-preserving forcing notions of size at most \omega_1 including all \omega-proper forcing notions and some proper but not \omega-proper 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 \omega-distributive 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.
• Version 1995-04-17_10 (28p) published version (22p)
Bib entry
@article{Sh:563,
author = {Jin, Renling and Shelah, Saharon},
title = {{Can a small forcing create Kurepa trees}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {85},
number = {1},
year = {1997},
pages = {47--68},
issn = {0168-0072},
mrnumber = {1443275},
mrclass = {03E35 (03E05 03E55)},
doi = {10.1016/S0168-0072(96)00018-8},
note = {\href{https://arxiv.org/abs/math/9504220}{arXiv: math/9504220}},
arxiv_number = {math/9504220}
}