11 found
Order:
See also
Carolin Antos
Universität Konstanz
  1.  47
    Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - forthcoming - Review of Symbolic Logic:1-50.
    A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  2.  33
    Conceptions of Infinity and Set in Lorenzen’s Operationist System.Carolin Antos - forthcoming - In Logic, Epistemology and the Unity of Science. Springer.
    In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  3. Class Forcing in Class Theory.Carolin Antos - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.), The Hyperuniverse Project and Maximality. 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   2 citations  
  4.  30
    Introduction to Special Issue on the Foundations of Mathematics.Carolin Antos, Neil Barton, Sy-David Friedman, Claudio Ternullo & John Wigglesworth - 2020 - Synthese 197.
    No categories
    Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5. The Hyperuniverse Project and Maximality.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.) - 2018 - Basel, Switzerland: Birkhäuser.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  6. Multiverse Conceptions in Set Theory.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo - 2015 - Synthese 192 (8):2463-2488.
    We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  7.  10
    Introduction.Carolin Antos, Neil Barton, Sy-David Friedman, Claudio Ternullo & John Wigglesworth - 2020 - Synthese 197 (2):469-475.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  8.  19
    Foundations of Higher-Order Forcing.Carolin Antos - 2018 - Bulletin of Symbolic Logic 24 (4):457-457.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  9.  1
    Hyperclass Forcing in Morse-Kelley Class Theory.Carolin Antos & Sy-David Friedman - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.), The Hyperuniverse Project and Maximality. Birkhäuser. pp. 17-46.
    In this article we introduce and study hyperclass-forcing in the context of an extension of Morse-Kelley class theory, called MK∗∗. We define this forcing by using a symmetry between MK∗∗ models and models of ZFC− plus there exists a strongly inaccessible cardinal. We develop a coding between β-models ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document} of MK∗∗ and transitive models M+ of SetMK∗∗ which will allow us to go from ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  10.  6
    Hyperclass Forcing in Morse-Kelley Class Theory.Carolin Antos & Sy-David Friedman - 2017 - Journal of Symbolic Logic 82 (2):549-575.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11. Multiverse Conceptions in Set Theory.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.), The Hyperuniverse Project and Maximality. Birkhäuser. pp. 47-73.
    We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark