All Questions
7 questions
2
votes
0
answers
44
views
Diamonds on supercompact $\kappa$ after a $\kappa$-c.c. forcing
Let $\kappa$ be supercompact. Then the (supercompact) Laver diamond holds at $\kappa$: There is $f:\kappa\to V_\kappa$ such that for all $\lambda\geq \kappa$ and $x\in H(\lambda^+)$ there is $j:V\to M$...
- 51
12
votes
0
answers
213
views
Is $\kappa \rightarrow [\kappa]^2_3$ the same as $\kappa \rightarrow [\kappa]^2_2$ for inaccessible $\kappa$
The principle $\kappa \rightarrow [\kappa]^2_\alpha$ states that whenever we have a coloring $c:[\kappa]^2\rightarrow \alpha$ there is $H \subset \kappa$ of size $\kappa$ s.t. $|c"[H]^2|<\alpha$.
...
- 490
11
votes
0
answers
490
views
$\Sigma^2_1$ and the Continuum Hypothesis
This is a follow up to Will Brian's answer to this recent question. In particular, quoting Brian:
"In fact, Paul Larson has pointed out to me that the statement "$\phi$ and $\phi^{-1}$ are conjugate"...
- 7,125
7
votes
1
answer
299
views
Consistency of Rado's conjecture with not CH
Rado's conjecture (one of many equivalent formulations) states: any non-special tree has a non-special subtree of cardinality $\aleph_1$.
"Special" means a tree can be decomposed into countably many ...
- 3,038
5
votes
1
answer
391
views
Adding large sets not containing countable ground model sets
The question is motivated by Toni's question "Approximation of infinite set in generic extension" (see Approximation of infinite set in generic extension).
Before I state the question, let me add ...
- 32.1k
7
votes
1
answer
950
views
Is there a monster behind the trees?
First Fix the following notation:
$\forall \kappa\in Card~~~Tp(\kappa):="\kappa~has~tree~property"$
The large cardinals as "monsters of heaven" live everywhere in the land of ...
user36136
8
votes
2
answers
1k
views
failure of $\square(\kappa)$ at an inaccessible $\kappa$
How can we force the failure of $\square(\kappa)$ at an inaccessible $\kappa$, where
$\square(\kappa)$ is defined as follows: There is a sequence $(C_i:i< \kappa)$ such that:
(1) $C_{i+1} = \{i\}$...
- 32.1k