Tagged Questions
5
votes
3answers
107 views
Questions on Fraenkel models
Halbeisen on page 172 contains a section entitled "The Second Fraenkel Model". The original paper by Fraenkel containing this model can be found here. I have several questions regarding this model and ...
3
votes
3answers
195 views
What do these old symbols from set theory mean? (Large E, $\cdot$ and $+$ for sets, and $\ \bar{\!\bar X}\,non\!\geqslant\frak n$)
So, I'm trying to prove the theorems in this paper by Tarski:
On Well-ordered Subsets of any Set, Fundamenta Mathematicae, vol.32 (1939), pp.176-183
but it is from 1939, and I don't recognize a few ...
2
votes
1answer
131 views
Did large cardinals exist before 1963?
I'm curious to know the history of the interaction between large cardinals and traveling to (creating) universes through forcing. The question arose because I understand that Peano Arithmatists ...
12
votes
0answers
108 views
Is Dover publishing Moore's book on the Axiom of Choice? [closed]
Dover is publishing a paperback edition of Gregory H. Moore's Zermelo's Axiom of Choice: Its Origins, Development, and Influence. It's supposed to come out March 20th and is available for pre-order at ...
1
vote
2answers
188 views
What did Cantor take to be the relationship between the countable ordinals and the power set of the naturals?
I've been told that Cantor sees a relationship between the countable ordinals (Cantor's second number class) and the powerset of the natural numbers.
I've read the "Grundlagen" a few times, but can't ...
4
votes
2answers
160 views
Analytic versus Analytical Sets
Browsing MathOverflow I came across a question about analytical sets. Through the discussion following a comment made by our very own Asaf, I learned that bold face $\mathbf{\Sigma^1_1}$ and light ...
14
votes
4answers
499 views
Why is the axiom of choice separated from the other axioms?
I don't know much about set theory or foundational mathematics, this question arose just out of curiosity. As far as I know, the widely accepted axioms of set theory is the Zermelo-Fraenkel axioms ...
2
votes
1answer
168 views
a question on stationary sets
$S\subset \lambda$ is called a stationary set if for any closed unbounded set $E$ of $\lambda$, then $S\cap E \neq \emptyset.$ Why do people give the name "stationary set" for the sets which has such ...
8
votes
2answers
211 views
The history of set-theoretic definitions of $\mathbb N$
What representations of the natural numbers have been used, historically, and who invented them? Are there any notable advantages or disadvantages?
I read about Frege's definition not long ago, ...
13
votes
1answer
638 views
About a paper of Zermelo
This about the famous article
Zermelo, E., Beweis, daß jede Menge wohlgeordnet werden kann, Math. Ann. 59 (4), 514–516 (1904),
available here. Edit: Springer link to the ...
51
votes
11answers
4k views
Why did mathematicians take Russell's paradox seriously?
Though I've understood the logic behind's Russell's paradox for long enough, I have to admit I've never really understood why mathematicians and mathematical historians thought it so important. Most ...
