Talk:Axiom of limitation of size
|WikiProject Mathematics||(Rated Start-class, Mid-priority)|
Added section "Zermelo's models and the axiom of limitation of size"
I added a new section "Zermelo's models and the axiom of limitation of size" because of my personal experience with the axiom. When I first heard about the axiom, my reaction was: "Why can't there be classes of different sizes? After all, the ordinals form a 'thin' class and the universal class is 'much thicker'." When I learned of Zermelo's models, it became clear why the axiom can be true.
So I've added a model-theoretic section to complement the current article (which concentrates on the implications of the axiom and its relationship to other axioms). My approach was to write an exposition of Zermelo's work in 3 parts: The first gives the reader an overall view and emphasizes two statements Zermelo proved (which in my exposition are Theorems 1 and 2). A more interested reader may like to see why these theorems are true for a simple model — this is covered in the subsection "The model Vω." This subsection naturally leads to the subsection "The models Vκ where κ is a strongly inaccessible cardinal." Zermelo handled the cases κ = ω and κ is a strongly inaccessible cardinal at the same time. However, Zermelo was writing a research article. I'm thinking of Wikipedia readers, and I realized that by dividing the exposition into 3 parts, each a bit harder than the previous, I'm catering to readers of different math levels and different interest levels. --RJGray (talk) 19:45, 3 February 2013 (UTC)