4 found
Sort by:
  1. Oliver Deiser (2011). An Axiomatic Theory of Well-Orderings. Review of Symbolic Logic 4 (2):186-204.
    We introduce a new simple first-order framework for theories whose objects are well-orderings (lists). A system ALT (axiomatic list theory) is presented and shown to be equiconsistent with ZFC (Zermelo Fraenkel Set Theory with the Axiom of Choice). The theory sheds new light on the power set axiom and on Gs axiom of constructibility. In list theory there are strong arguments favoring Gs axiom, while a bare analogon of the set theoretic power set axiom looks artificial. In fact, there is (...)
    No categories
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  2. Oliver Deiser (2011). On the Development of the Notion of a Cardinal Number. History and Philosophy of Logic 31 (2):123-143.
    We discuss the concept of a cardinal number and its history, focussing on Cantor's work and its reception. J'ay fait icy peu pres comme Euclide, qui ne pouvant pas bien >faire< entendre absolument ce que c'est que raison prise dans le sens des Geometres, definit bien ce que c'est que memes raisons. (Leibniz) 1.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  3. Oliver Deiser & Dieter Donder (2003). Canonical Functions, Non-Regular Ultrafilters and Ulam's Problem on Ω. Journal of Symbolic Logic 68 (3): 713- 739.
    Our main results are: Theorem 1. Con(ZFC + "every function $f : \omega_{1} \rightarrow \omega_1$ is dominated by a canonical function") implies Con(ZFC + "there exists an inaccessible limit of measurable cardinals"). [In fact equiconsistency holds.] Theorem 3. Con(ZFC + "there exists a non-regular uniform ultrafilter on ω1") implies Con(ZFC + "there exists an inaccessible stationary limit of measurable cardinals"). Theorem 5. Con (ZFC + "there exists an $\omega_{1}-sequence$ T of $\omega_{1}-complete$ uniform filters on ω1 s.t. every $A \subseteq \omega_1$ (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  4. Oliver Deiser & Hans-Dieter Donder (2003). Canonical Functions, Non-Regular Ultrafilters and Ulam's Problem on 1. Journal of Symbolic Logic 68 (3):713-739.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation