58 research outputs found
Tarski's Q-relation algebras and Thompson's groups
The connections between Tarski's Q-relation algebras and Thompson's groups F,
T, V, and monoid M are reviewed here, along with Jonsson-Tarski algebras, fork
algebras, true pairing algebras, and tabular relation algebras. All of these
are related to the finitization problem and Tarski's formalization of set
theory without variables. Most of the technical details occur in the variety of
J-algebras, which is obtained from relation algebras by omitting union and
complementation and adopting a set of axioms created by Jonsson. Every relation
algebra or J-algebra that contains a pair of conjugated quasiprojections
satisfying the Domain and Unicity conditions, such as those that arise from
J\'onsson-Tarski algebras or fork algebras, will also contain homomorphic
images of F, T, V, and M. The representability of tabular relation algebras is
extended here to J-algebras, using a notion of tabularity equivalent among
relation algebras to the original definition.Comment: 64 pages, 4 figures, 1 tabl
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