The boolean-algebras tag has no usage guidance.

**16**

votes

**0**answers

741 views

### Which complete Boolean algebras arise as the algebras of projections of commutative von Neumann algebras?

Projections in an arbitrary commutative von Neumann algebra form a complete Boolean algebra.
Moreover, a morphism of commutative von Neumann algebras induces
a continuous morphism of the corresponding ...

**8**

votes

**0**answers

578 views

### Full conditional probabilities and versions of AC?

A probability is a finitely additive measure on a boolean algebra with total measure $1$.
A function $P:\scr B \times (\scr B - \{ 0 \})$ is a full conditional probability on $\scr B$ (for a boolean ...

**10**

votes

**0**answers

434 views

### Existence of a regular subposet which collapses everything except the top cardinal

Suppose $\delta$ is an inaccessible cardinal, and $\mathbb{P}$ is the Levy Collapse $\text{Col}(\kappa, \delta)$ which adds a surjection from $\kappa \to \delta$ (for some regular $\kappa < \delta$)...

**2**

votes

**2**answers

514 views

### Embedding a brouwerian lattice into a boolean lattice

I have already asked a similar question at
http://math.stackexchange.com/questions/470704/can-a-brouwerian-lattice-be-extended-into-a-boolean-algebra
but have received no answer.
Sorry, I ask a ...

**6**

votes

**1**answer

216 views

### On intermediate transitive models for ZFC between M an M[G]

Let $P$ be a forcing notion. Let $B(P)$ be the boolean completion of $P$ and $i : P \rightarrow B(P)$ be the corresponding dense embedding (in $B(P)^{+}$). Let $G$ be $B(P)$-generic over $M$, the ...

**3**

votes

**2**answers

192 views

### Chain of ideals in a BA

Suppose $\mathfrak{A}$ is a Boolean algebra and $\mathfrak{J}$ is chain of ideals in $\mathfrak{A}$ ordered by inclusion such that none of its elements is countably generated. Clearly, the union $\...

**1**

vote

**5**answers

652 views

### Is there such a thing as the sigma-completion of a Boolean algebra?

Hi all,
Suppose that $\mathcal{B}$ is a Boolean algebra. It there a way to extend $\mathcal{B}$ to a smallest Boolean algebra $\mathcal{B}'$ that contains an isomorphic copy of $\mathcal{B}$ and is ...

**2**

votes

**2**answers

390 views

### The category of Boolean-valued models associated to a model of ZFC

This is related to my previous question here, and indirectly motivated by Andreas Blass intriguing answer therein:
start from a ZF transitive model $M$, and consider the category $CBA(M)$ of ...

**2**

votes

**1**answer

192 views

### Sigma-complete Lindenbaum algebras? [closed]

Is there any calculus whose algebraization is a sigma-complete Lindenbaum algebra, i.e., a sigma-complete Boolean algebra after identification of equivalent formulas?

**1**

vote

**1**answer

145 views

### Finitely additive measures on Boolean algebras of regular open subsets: Is there a relationship with Borel measures? A theory of integration?

Let $\mathcal{X}$ be a topological space. An open subset $\mathcal{R}\subseteq\mathcal{X}$ is regular if it is the interior of its own closure. The intersection of two regular open sets is regular. ...

**1**

vote

**2**answers

254 views

### Question on separability of a measure

Following this question here this question come to mind.
Consider a measured σ-algebra $(S,\mu)$ . Assume that μ is normalized to have total weight 1, and that S is complete (contains all subsets of ...