All Questions
6 questions
3
votes
0
answers
152
views
Why are the sharps of sets of big ordinals not in $\mathcal{P}(\omega)$?
In his talk A Condensed History of Condensation, Welch presents the following recursive sharp function, that is total when all sharps exist:
\begin{align*}
\# \colon ON &\to \mathcal{P}(ON) \\
\...
- 421
8
votes
1
answer
591
views
Is there an abstract logic that defines the mantle?
It is a known result by Scott and Myhill that the second-order version of $L$ yields $\mathrm{HOD}$.
Recently, Kennedy, Magidor, and Väänänen (Inner models from extended logics: Part I and II) ...
- 3,042
3
votes
4
answers
542
views
Is a sentence true for two substructures also true for their intersection? [closed]
Let $L$ be a first order language and $M$ an interpretation of $L$.
If $A$ and $B$ are two substructures of $M$ and their intersection $C=A\cap B\ne \emptyset$, then is it the case that every sentence ...
- 33
7
votes
1
answer
363
views
Is the consistency of $\mathcal{L}_{\infty\omega}$-sentences absolute?
The question is exactly that of the title. Suppose $\varphi\in V$ is an $\mathcal{L}_{\infty\omega}$-sentence, and $W$ is an inner model of $V$ such that $\varphi\in W$. Is the statement
$\varphi$ ...
- 21.2k
3
votes
1
answer
297
views
Do inner models of unique measurable cardinals have a regular behavior? (Edited and Revised Version)
We know that if $\kappa$ is a measurable cardinal and $\mu$ be a two-valued non-trivial$\kappa$-additive measure on it then the corresponding inner model produced by ...
user36136
7
votes
2
answers
377
views
Is there an inner model between two distinct inner models of ZFC?
Definition (1): An inner model of $ZFC$ is a tarnsitive proper class model of $ZFC$ which contains all ordinal numbers. Informally we denote the collection of all inner ...
user36136