Every recursive boolean algebra is isomorphic to one with incomplete atoms

Every Low 2 Boolean Algebra Has a Recursive Copy

The degree of a structure si is the Turing degree of its open diagram £»(j/) , coded as a subset of a>. Implicit in the definition is a particular presentation of the structure; the degree is not an isomorphism invariant. We prove that if a Boolean algebra si has a copy of low 2 degree, then there is a recursive Boolean algebra 33 which is isomorphic to si . This builds on work of Downey and Jo...

A Model in Which Every Boolean Algebra Has Many Subalgebras

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subsetA such that 2|A| = 2|B|. This implies in particular that B has 2|B| subalgebras. We also discuss some more general problems about subalgebras and free subsets of an algebra. The result on the number of subalgebras in a Boolean algebra solves a question of Monk from...

Every Concept Lattice With Hedges Is Isomorphic To Some Generalized Concept Lattice

We show the relationship between two different types of common platforms of till known fuzzifications of a concept lattice, namely that the notion of a concept lattice with hedges is a special case of our generalized concept lattice.

A Nonseparable Amenable Operator Algebra Which Is Not Isomorphic to a C∗-algebra

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C∗-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open problem.

Process Algebra with Recursive