1
vote
2answers
73 views

Construct countable Boolean algebra

How can I construct a countably infinite Boolean algebra with $n$ atoms, for $n \in \mathbb{N}$?
6
votes
1answer
178 views

Non-isomorphic countable Boolean algebras

I'm trying to solve the next exercise: Construct a sequence $\mathcal{B}_0,\mathcal{B}_1, \ldots$ of countable Boolean algebras such that for all $m \neq n$ then $\mathcal{B}_0 \ncong \mathcal{B}_1$. ...
1
vote
2answers
147 views

Boolean algebra spectrum

The first-order spectrum of a theory, is the set of cardinalities of its finite models. Finite models of Boolean algebras are informally n-dimensional cubes, therefore boolean algebra spectrum is the ...
10
votes
1answer
142 views

Saturated Boolean algebras in terms of model theory and in terms of partitions

Let $\kappa$ be an infinite cardinal. A Boolean algebra $\mathbb{B}$ is said to be $\kappa$-saturated if there is no partition (i.e., collection of elements of $\mathbb{B}$ whose pairwise meet is $0$ ...
4
votes
1answer
209 views

Lindenbaum algebra is a free algebra

The following is a continuation of this question. I would like to prove that the Lindenbaum algebra is a free algebra. Hopefully I would like to hear hints on how to proceed in the 'right' ...
1
vote
0answers
180 views

Can the reduced product construction generate boolean-valued models?

In model theory, the reduced product construction contains a collection of structures or models, a set I that indexes the collection, and a filter U on I. Ultraproducts are a special case of reduced ...
6
votes
2answers
160 views

Axioms for atomless Boolean algebras

I'm embarrassed to be asking, but: "Write down a set of axioms for the theory of atomless Boolean algebras." This is Exercise 1.14 in Chapter 9 of "Models and Ultraproducts" by Bell and Slomson. I'm ...
6
votes
2answers
195 views

Boolean algebras without atoms

Why is the theory of Boolean algebras without atoms $\omega$-categoric?