# Tagged Questions

94 views

### When are the congruence lattices nicer?

This is a purely idle question, but one I'm increasingly interested the more thought I put into it: For $\mathcal{A}$ a universal algebra (that is, nonempty set together with some named functions), a ...
235 views

### Is every Heyting algebra the Lindenbaum algebra of an intuitionistic first order theory?

This question comes after the comments in the recent related question Sigma-complete Lindenbaum algebras?, but in its current form is sufficiently different in my opinion, and so I decided to follow ...
368 views

### Compactness and completeness in Gödel logic

The standard proof of the completeness theorem in first-order Gödel logic is based on a first-order countable language. I want to know that is there any proof of the completeness theorem in ...
276 views

### Constructing the Stone Space of a Distributive Lattice

Does anyone have a good reference for the method of giving a topology to a distributive lattice as outlined in M.H. Stone's "Topological representation of distributive lattices and Brouwerian logics"? ...
305 views

### Complete De Morgan algebra

Recall that an algebra $(A,\sim)$ is a De Morgan algebra if $A$ is a bounded distributive lattice and $\sim$ is a unary operation which satisfies: ${\sim} (x\vee y)={\sim} x\wedge {\sim} y$ and ...
569 views

### additive functions on a lattice

Given a lattice $L$. Can one classify all functions $f:L\rightarrow \mathbb{R}$, that satisfy $f(a \wedge b)+f(a\vee b) = f(a)+f(b)$. Some examples are the the set of all finite subsets of a given ...
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### Can the Knaster-Tarski theorem be proved using the Schroeder-Bernstein theorem?

The reverse can be done easily and the proof is well known I am wondering if the exact same argument can be used to prove reverse as well.
615 views

### `Topos' with alternate subobject lattice?

We know that for any topos E, and for any object A in E, the subobjects of A, Sub(A), form a Heyting lattice. Does anybody know of any sort of modification of the definition of a topos that makes ...