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

Yorioka Teruyuki | Zendy

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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].

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