This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Siblings:
4 found
Search inside:
(import / add options)   Sort by:
  1. Jonas R. Becker Arenhart (2012). Finite Cardinals in Quasi-Set Theory. Studia Logica 100 (3):437-452.
    Quasi-set theory is a ZFU-like axiomatic set theory, which deals with two kinds of ur-elements: M-atoms, objects like the atoms of ZFU, and m-atoms, items for which the usual identity relation is not defined. One of the motivations to advance such a theory is to deal properly with collections of items like particles in non-relativistic quantum mechanics when these are understood as being non-individuals in the sense that they may be indistinguishable although identity does not apply to them. According to (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  2. Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...)
    Remove from this list |
    Translate to English
    | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  3. Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
    In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  4. Michael D. Potter (2004). Set Theory and its Philosophy: A Critical Introduction. Oxford University Press.
    Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation