Towers, mad families, and unboundedness

We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are [Formula: see text] -Canjar for any countably directed unbounded family [Formula: see text] of the gro...

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Detalles Bibliográficos
Autores principales: Fischer, Vera, Koelbing, Marlene, Wohofsky, Wolfgang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10227169/
https://www.ncbi.nlm.nih.gov/pubmed/37260528
http://dx.doi.org/10.1007/s00153-023-00861-x
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author Fischer, Vera
Koelbing, Marlene
Wohofsky, Wolfgang
author_facet Fischer, Vera
Koelbing, Marlene
Wohofsky, Wolfgang
author_sort Fischer, Vera
collection PubMed
description We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are [Formula: see text] -Canjar for any countably directed unbounded family [Formula: see text] of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that [Formula: see text] in every extension by the above forcing notions.
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spelling pubmed-102271692023-05-31 Towers, mad families, and unboundedness Fischer, Vera Koelbing, Marlene Wohofsky, Wolfgang Arch Math Log Article We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are [Formula: see text] -Canjar for any countably directed unbounded family [Formula: see text] of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that [Formula: see text] in every extension by the above forcing notions. Springer Berlin Heidelberg 2023-02-12 2023 /pmc/articles/PMC10227169/ /pubmed/37260528 http://dx.doi.org/10.1007/s00153-023-00861-x Text en © The Author(s) 2023, corrected publication 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Fischer, Vera
Koelbing, Marlene
Wohofsky, Wolfgang
Towers, mad families, and unboundedness
title Towers, mad families, and unboundedness
title_full Towers, mad families, and unboundedness
title_fullStr Towers, mad families, and unboundedness
title_full_unstemmed Towers, mad families, and unboundedness
title_short Towers, mad families, and unboundedness
title_sort towers, mad families, and unboundedness
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10227169/
https://www.ncbi.nlm.nih.gov/pubmed/37260528
http://dx.doi.org/10.1007/s00153-023-00861-x
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