Switch to: Citations

Add references

You must login to add references.
  1. Class Forcing in Class Theory.Carolin Antos - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.), The Hyperuniverse Project and Maximality. Basel, Switzerland: Birkhäuser. pp. 1-16.
    In this article we show that Morse-Kelley class theory provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$$$ \end{document} of MK, the main result being that the Definability Lemma can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does not hold for (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Class forcing, the forcing theorem and Boolean completions.Peter Holy, Regula Krapf, Philipp Lücke, Ana Njegomir & Philipp Schlicht - 2016 - Journal of Symbolic Logic 81 (4):1500-1530.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  • What is the theory without power set?Victoria Gitman, Joel David Hamkins & Thomas A. Johnstone - 2016 - Mathematical Logic Quarterly 62 (4-5):391-406.
    We show that the theory, consisting of the usual axioms of but with the power set axiom removed—specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every set can be well‐ordered—is weaker than commonly supposed and is inadequate to establish several basic facts often desired in its context. For example, there are models of in which ω1 is singular, in which every set of reals is countable, yet ω1 exists, in which there are sets of (...)
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  • Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
    We discuss the problem of finding forcing posets which introduce closed unbounded subsets to a given stationary set.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   30 citations