Switch to: References

Add citations

You must login to add citations.
  1. Varieties of Class-Theoretic Potentialism.Neil Barton & Kameryn J. Williams - 2024 - Review of Symbolic Logic 17 (1):272-304.
    We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Modal Model Theory.Joel David Hamkins & Wojciech Aleksander Wołoszyn - 2024 - Notre Dame Journal of Formal Logic 65 (1):1-37.
    We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathematically natural notions of possibility and necessity. A statement φ is possible in a structure (written φ) if φ is true in some extension of that structure, and φ is necessary (written φ) if it is true in all extensions of the structure. A principal case for us will be the class Mod(T) (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Every Countable Model of Arithmetic or Set Theory has a Pointwise-Definable End Extension.Joel David Hamkins - forthcoming - Kriterion – Journal of Philosophy.
    According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of set theory, in which every individual is definable without parameters, challenges this conclusion. In this article, I introduce a flexible new method for constructing pointwise-definable models of arithmetic and set theory, showing furthermore that every countable model of Zermelo-Fraenkel ZF set theory and of (...)
    Download  
     
    Export citation  
     
    Bookmark