A Boolean algebra without proper automorphisms

A Complete Boolean Algebra That Has No Proper Atomless Complete Sublagebra

There exists a complete atomless Boolean algebra that has no proper atomless complete subalgebra. An atomless complete Boolean algebra B is simple [5] if it has no atomless complete subalgebra A such that A 6= B. The question whether such an algebra B exists was first raised in [8] where it was proved that B has no proper atomless complete subalgebra if and only if B is rigid andminimal. For mo...

Jordan Automorphisms on a Semisimple Banach Algebra

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

Ternary Boolean Algebra

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...

Free Boolean Algebra

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...