Tagged Questions
2
votes
2answers
115 views
Forcing Question about a sequence of functions from $\aleph_{0}$ into $2 = \{0, 1\}$
I'm trying to go through Timothy Chow's A Beginner's Guide to Forcing (arxiv pdf).
My particular question is about the first paragraph of Section $5$ (on p. $7$ of the above pdf).
First, my vague ...
2
votes
1answer
109 views
Infitive distributive law in boolean valued models
I'm posting the problem 2.14 and 2.15 of the book "Set theory" of J.L. Bell. These problem are proposed after the forcing relation chapter and I'm new in this kind of stuff, so I have some little ...
1
vote
3answers
115 views
Question about models, cardinalities and collapsing
I have a (seeming) contradiction and I can't seem to figure out the (obvious) mistake in my reasoning. The following (related to my previous question):
(1) $\omega$, defined to be the least infinite ...
2
votes
1answer
131 views
When collapsing a cardinal, what ordinal does it become?
Work in $V$. Let $P = \text{Col}(\omega, \omega_1)$ and suppose that $G$ is generic for $P$ over $V$. Then $V[G]\models |\omega_1^V|=\aleph_0$ and $\omega_2^V=\aleph_1$. In particular, ...
7
votes
2answers
257 views
What does Martin's Maximum imply for $P(\mathbb{R})$?
Prompted by this question: of course Godel's constructibility axiom implies that $P(S)$ is minimal for any set $S$ and so handily answers the question of the size of the power set of the continuum in ...
