A note on a forcing related to the S‐space problem in the extension with a coherent Suslin tree

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].