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Interpreting reflexive theories in finitely many axioms

V. Shavrukov — 1997

Fundamenta Mathematicae

For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of 1 (as well as 1 ) sentences π such that GB interprets ZF+π is Σ 3 0 -complete.

Monoid presentations of groups by finite special string-rewriting systems

Duncan W. ParkesV. Yu. ShavrukovRichard M. Thomas — 2010

RAIRO - Theoretical Informatics and Applications

We show that the class of groups which have monoid presentations by means of finite special [λ]-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

Monoid presentations of groups by finite special string-rewriting systems

Duncan W. ParkesV. Yu. ShavrukovRichard M. Thomas — 2004

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that the class of groups which have monoid presentations by means of finite special [ λ ] -confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

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