# Sh:563

- Jin, R., & Shelah, S. (1997).
*Can a small forcing create Kurepa trees*. Ann. Pure Appl. Logic,**85**(1), 47–68. arXiv: math/9504220 DOI: 10.1016/S0168-0072(96)00018-8 MR: 1443275 -
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} }