2018/10/23 by Osvaldo Guzmán, Guzman, Osvaldo · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1810.09680
openalex publication_date 2018/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the Ph.D. thesis of the author, which was written under the supervision of Michael Hrušák at UNAM. The main contributions of this thesis are the following: There is a +-Ramsey \textsfMAD family. This answers an old question of Michael Hrušák. There are no P-points in the Silver model, answering a question of Michael Hrušák (this is joint work with David Chodounský. The statement \textquotedblleft There are no P-points\textquotedblright is consistent with the continuum being arbitrarily large, this answers an open question regarding P-points. Every Miller indestructible \textsfMAD family is +-Ramsey. This improves a result of Hrušák and Garc'ıa Ferreira. A Borel ideal is Shelah-Steprāns if and only if it is Katětov above \textsfFIN×\textsfFIN. This entails that Shelah-Steprāns \textsfMAD families have very strong indestructibility properties. Cohen indestructible \textsfMAD families exist generically if and only if \mathfrakb=c. The equality \textsfnon( M) =ω1 implies the ( ∗) principle of Sierpiński. This answers a question of Arnie Miller.