Switch to: References

Add citations

You must login to add citations.
  1. Some transfinite natural sums.Paolo Lipparini - 2018 - Mathematical Logic Quarterly 64 (6):514-528.
    We study a transfinite iteration of the ordinal Hessenberg natural sum obtained by taking suprema at limit stages. We show that such an iterated natural sum differs from the more usual transfinite ordinal sum only for a finite number of iteration steps. The iterated natural sum of a sequence of ordinals can be obtained as a mixed sum (in an order‐theoretical sense) of the ordinals in the sequence; in fact, it is the largest mixed sum which satisfies a finiteness condition. (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Asymptotic analysis of skolem’s exponential functions.Alessandro Berarducci & Marcello Mamino - 2020 - Journal of Symbolic Logic:1-25.
    Skolem studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant $1$, the identity function ${\mathbf {x}}$, and such that whenever f and g are in the set, $f+g,fg$ and $f^g$ are in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz computed the order type of the fragment below $2^{2^{\mathbf {x}}}$. Here we prove that (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • Asymptotic analysis of skolem’s exponential functions.Alessandro Berarducci & Marcello Mamino - 2022 - Journal of Symbolic Logic 87 (2):758-782.
    Skolem studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant $1$, the identity function ${\mathbf {x}}$, and such that whenever f and g are in the set, $f+g,fg$ and $f^g$ are in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz computed the order type of the fragment below $2^{2^{\mathbf {x}}}$. Here we prove that (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•