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Sep
24 |
awarded | Autobiographer |
Mar
21 |
awarded | Yearling |
Oct
29 |
awarded | Popular Question |
May
24 |
asked | Amalgamation of two ccc algebras may collapse the continuum |
Jun
14 |
comment |
Blackbox Theorems
Another result of Shelah which may fit in this list is the Main Gap Theorem. |
May
16 |
comment |
How badly does compactness fail in $\mathcal{L}_{\omega_1\omega}$?
If you weaken your demands to just having the upward Lowenheim-Skolem property, then Morley proved that the Hanf number of $L_{\omega_1, \omega}$ is $\beth_{\omega_1}$. |
Jan
26 |
awarded | Yearling |
Nov
20 |
comment |
The purview or scope of set theory qua set theory
This is not exactly an answer, but I think that this text might be relevant to your question: shelah.logic.at/files/E16.pdf |
Oct
2 |
comment |
Why are some axioms preserved in generic extensions?
It's worth noting that the answer may depend on large cardinal assumptions. For example, by a result of Woodin, the existence of class many measurable Woodin cardinals implies that Sigma-2-1 formulas that are true in one forcing extension are true in all forcing extensions satisfying CH (see the paper of Illias Farah for further discussion). |
Aug
26 |
answered | The concept of Duality |
Jul
31 |
comment |
Dual covering theorem
Thanks, Andres. :) |
Jul
31 |
accepted | Dual covering theorem |
Jul
30 |
revised |
Dual covering theorem
added 70 characters in body |
Jul
30 |
asked | Dual covering theorem |
May
9 |
comment |
Most memorable titles
How can we talk about sweetness without mentioning Saccharinity? shelah.logic.at/files/859.pdf :) |
Jan
26 |
awarded | Yearling |
Nov
26 |
comment |
The history of Proper Forcing
I believe that the initial motivations for proper forcing are well explained throughout Shelah's book. If you want a brief look at the evolution of the subject, a good place to start reading at is the "Proper forcing" chapter in the handbook of set theory (written by Uri Abraham). Regarding the open problems, you can check this paper: shelah.logic.at/files/666.pdf |
Nov
21 |
comment |
Characterizing forcings that don't add any dominating reals
@Stefan: Yes, it means "there is no f in V dominating the new real". @Justin: The above result relies quite strongly on the absoluteness properties of Suslin forcing. I'm not aware of a similar result without any definability assumption. |
Nov
21 |
answered | Characterizing forcings that don't add any dominating reals |
Oct
2 |
comment |
$\kappa$-scales and the continuum
As Francois mentioned, b=d implies the existence of a scale. Now, it's worth noting that Martin's axiom implies the above equality (hence the existence of a scale). |