Switch to: References

Add citations

You must login to add citations.
  1. The tree property and the continuum function below.Radek Honzik & Šárka Stejskalová - 2018 - Mathematical Logic Quarterly 64 (1-2):89-102.
    We say that a regular cardinal κ,, has the tree property if there are no κ‐Aronszajn trees; we say that κ has the weak tree property if there are no special κ‐Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal,, is consistent with an arbitrary continuum function below which satisfies,. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal,, is consistent with an (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Global singularization and the failure of SCH.Radek Honzik - 2010 - Annals of Pure and Applied Logic 161 (7):895-915.
    We say that κ is μ-hypermeasurable for a cardinal μ≥κ+ if there is an embedding j:V→M with critical point κ such that HV is included in M and j>μ. Such a j is called a witnessing embedding.Building on the results in [7], we will show that if V satisfies GCH and F is an Easton function from the regular cardinals into cardinals satisfying some mild restrictions, then there exists a cardinal-preserving forcing extension V* where F is realised on all V-regular (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • A Laver-like indestructibility for hypermeasurable cardinals.Radek Honzik - 2019 - Archive for Mathematical Logic 58 (3-4):275-287.
    We show that if \ is \\)-hypermeasurable for some cardinal \ with \ \le \mu \) and GCH holds, then we can extend the universe by a cofinality-preserving forcing to obtain a model \ in which the \\)-hypermeasurability of \ is indestructible by the Cohen forcing at \ of any length up to \ is \\)-hypermeasurable in \). The preservation of hypermeasurability is useful for subsequent arguments. The construction of \ is based on the ideas of Woodin and Cummings :1–39, (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Capturing sets of ordinals by normal ultrapowers.Miha E. Habič & Radek Honzík - 2023 - Annals of Pure and Applied Logic 174 (6):103261.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • A Power Function with a Fixed Finite Gap Everywhere.Carmi Merimovich - 2007 - Journal of Symbolic Logic 72 (2):361 - 417.
    We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2κ = κ⁺ⁿ together with 2λ = λ⁺ⁿ for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible. When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2λ = λ+n for all cardinals λ.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations