Switch to: References

Add citations

You must login to add citations.
  1. What Model Companionship Can Say About the Continuum Problem.Giorgio Venturi & Matteo Viale - forthcoming - Review of Symbolic Logic:1-40.
    We present recent results on the model companions of set theory, placing them in the context of a current debate in the philosophy of mathematics. We start by describing the dependence of the notion of model companionship on the signature, and then we analyze this dependence in the specific case of set theory. We argue that the most natural model companions of set theory describe (as the signature in which we axiomatize set theory varies) theories of $H_{\kappa ^+}$, as $\kappa (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Are Large Cardinal Axioms Restrictive?Neil Barton - 2023 - Philosophia Mathematica 31 (3):372-407.
    The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation