Steven Givant | Mills College at Northeastern University (original) (raw)

Papers by Steven Givant

The Journal of Symbolic Logic, 1994

ABSTRACT

The Journal of Symbolic Logic, 1995

Memoirs of the American Mathematical Society, 1997

... Martin W. Liebeck and Gary M. Seitz, Reductive subgroups of exceptional algebraic groups, 199... more ... Martin W. Liebeck and Gary M. Seitz, Reductive subgroups of exceptional algebraic groups, 1996 579 Samuel Kaplan, Lebesgue theory in ... Society Number 604 Decision Problems for Equational Theories of Relation Algebras Hajnal Andreka Steven Givant Istvan Nemeti March ...

Annals of Pure and Applied Logic, 1994

We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but... more We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for (uncountable) universal theories T , that if T is κ-unique for one uncountable κ, then it is κ-unique for every uncountable κ; in particular, it is categorical in powers greater than the cardinality of T .

Algebra Universalis, 1999

extended the notion of the completion of a Boolean algebra to Boolean algebras with operators. Un... more extended the notion of the completion of a Boolean algebra to Boolean algebras with operators. Under the assumption that the operators of such an algebra A are completely additive, he showed that the completion of A always exists and is unique up to isomorphisms over A. Moreover, strictly positive equations are preserved under completions: a strictly positive equation that holds in A must hold in the completion of A.

algebra universalis, 1997

Algebra universalis, 2012

We give a new proof of a theorem due to Maddux and Tarski that every functionally dense relation ... more We give a new proof of a theorem due to Maddux and Tarski that every functionally dense relation algebra is representable. Our proof is very close in spirit to the original proof of the theorem of Jónsson and Tarski that atomic relation algebras with functional atoms are representable. We prove that a simple, functionally dense relation algebra is either atomic or atomless, and that every functionally dense relation algebra is essentially isomorphic to a direct product B × C, where B is a direct product of simple, functionally dense relation algebras each of which is either atomic or atomless, and C is a functionally dense relation algebra that is atomless and has no simple factors at all. We give several new structural descriptions of all atomic relation algebras with functional atoms. For example, each such algebra is essentially isomorphic to an algebra of matrices with entries from the complex algebra of some group. Finally, we construct examples of functionally dense relation algebras that are atomless and simple, and examples of functionally dense relation algebras that are atomless and have no simple factors at all.

Annals of Pure and Applied Logic, 1998

Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must... more Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable (as a cylindric set algebra). This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin- .