**6**

votes

**1**answer

196 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
...

**3**

votes

**1**answer

178 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 ...

**5**

votes

**2**answers

222 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 ...

**4**

votes

**1**answer

282 views

### Lattice of differences between ultrafilters

Consider two ultrafilters, $U$ and $V$, on the same cardinal $\kappa$. Let $D(U, V)=\lbrace X\subseteq \kappa: X\in U-V\rbrace$; clearly $D(U, V)$ is a lattice under $\subseteq, \cap, \cup $ since the ...