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Jan
7 |
answered | Can Sacks forcing add a Cohen generic real over $L$? |
Jan
5 |
comment |
Forcing the negation of CH without adding Cohen reals over L
Does this work if the ground model is something other than L? Can Sacks forcing over a model of CH containing no L-Cohen reals add an L-Cohen real? |
Dec
14 |
awarded | Custodian |
Nov
17 |
awarded | Popular Question |
Nov
13 |
accepted | Club-guessing at $\omega_2$ |
Nov
13 |
comment |
Club-guessing at $\omega_2$
Nice! This is exactly what I needed. |
Nov
13 |
asked | Club-guessing at $\omega_2$ |
Nov
8 |
answered | Is there a modification of Martin's Axiom which admits non-measurable sets of size less than continuum? |
Oct
30 |
comment |
PCF conjecture and fixed points of the $\aleph$-function
Mohammed, do you know off hand if the cardinal involved can be the least fixed point? |
Oct
29 |
comment |
PCF conjecture and fixed points of the $\aleph$-function
That would be a huge advance for sure, and much more difficult! |
Oct
21 |
comment |
The cofinality of $(\mathbb{N}^\kappa,\le)$ for uncountable $\kappa$?
@BoazTsaban: Jech's Chapter 29 mentions that the question of whether $f(\aleph_1)<2^{\aleph_1}$ is consistent is open, and I seem to recall that the question was also mentioned in the original "green version" of his book from 1978. |
Oct
18 |
comment |
The cofinality of $(\mathbb{N}^\kappa,\le)$ for uncountable $\kappa$?
Should have said "stronger implication" as the assumption is weaker... |
Oct
18 |
comment |
The cofinality of $(\mathbb{N}^\kappa,\le)$ for uncountable $\kappa$?
Just observe that the cofinality of $([\aleph_1]^{\aleph_0},\subseteq)$ is $\aleph_1$, as witnessed by initial segments. Same holds for all the $\aleph_n$ by induction. |
Oct
18 |
comment |
The cofinality of $(\mathbb{N}^\kappa,\le)$ for uncountable $\kappa$?
If the weakened implication in (2) holds then we would have $f(\aleph_1)=2^{\aleph_1}$ in ZFC. |
Oct
16 |
comment |
$\kappa$-support iterations of $<\kappa$-strategically closed forcing
That would indeed be silly: the result is folklore, and they include in a section recalling some standard facts. They prove the result for the same reason I asked for a reference: we need that the canonical strategy has some nice properties, and it is convenient to have a place to send a reader wanting to see some details. |
Oct
15 |
answered | $\kappa$-support iterations of $<\kappa$-strategically closed forcing |
Oct
1 |
comment |
$\kappa$-support iterations of $<\kappa$-strategically closed forcing
Sure. I was hoping to just be able to point somewhere if it were already written up. |
Sep
30 |
comment |
$\kappa$-support iterations of $<\kappa$-strategically closed forcing
Support preserving is one thing that I want, The other main thing is that if we're working in an $H(\chi)$ with a fixed well-ordering hanging around, then the obvious strategy is "canonical" if we use the well-ordering to make choices when we have to. |
Sep
30 |
comment |
$\kappa$-support iterations of $<\kappa$-strategically closed forcing
Yep, the straightforward proof works fine, and that's why the published proofs are all of the form "just like the $\kappa$-closed case''. I was just hoping that I had someplace to point readers rather than writing up the proof and noticing that a couple of other things happen. |
Sep
30 |
asked | $\kappa$-support iterations of $<\kappa$-strategically closed forcing |