Premium
A note on a forcing related to the S‐space problem in the extension with a coherent Suslin tree
Author(s) -
Yorioka Teruyuki
Publication year - 2015
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201300066
Subject(s) - mathematics , forcing (mathematics) , extension (predicate logic) , tree (set theory) , topology (electrical circuits) , space (punctuation) , basis (linear algebra) , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , geometry , computer science , programming language , operating system
One of the main problems about error ( S ) is that whether a coherent Suslin tree forces that there are no S‐spaces under error ( S ) . We analyze a forcing notion related to this problem, and show that under error ( S ) , S forces that every topology on ω 1 generated by a basis in the ground model is not an S‐topology. This supplements the previous work due to Stevo Todorčević [25].