Every low Boolean algebra is isomorphic to a recursive one
نویسندگان
چکیده
منابع مشابه
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...
متن کاملA 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...
متن کاملA 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.
متن کاملEvery projective Schur algebra is Brauer equivalent to a radical abelian algebra
We prove that any projective Schur algebra over a field K is equivalent in Br(K) to a radical abelian algebra. This was conjectured in 1995 by Sonn and the first author of this paper. As a consequence we obtain a characterization of the projective Schur group by means of Galois cohomology. The conjecture was known for algebras over fields of positive characteristic. In characteristic zero the c...
متن کاملEvery Quasigroup Is Isomorphic to a Subdirectly Irreducible Quasigroup modulo Its Monolith
Every quasigroup (loop, Bol loop, group, respectively) is isomorphic to the factor of a subdirectly irreducible quasigroup (loop, Bol loop, group, respectively) over its monolithic congruence.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1994-1203984-4