Finitely generated groups with automatic presentations
... In a sense, the answer depends on how you are considering the structures. As noted in [10], the main difference is that of substructures: the substructures of groups as structures (G, ◦) need only be subsemigroups, whereas, with (G, ◦, e, −1 ), they must be subgroups. For our purposes, we needn’t be ...
... In a sense, the answer depends on how you are considering the structures. As noted in [10], the main difference is that of substructures: the substructures of groups as structures (G, ◦) need only be subsemigroups, whereas, with (G, ◦, e, −1 ), they must be subgroups. For our purposes, we needn’t be ...
Transfinite progressions: A second look at completeness.
... than an extension by n-reflection, unless the same formula is used to define the axioms of T in both extensions. (This is a consequence of the fact, which will emerge below, that definitions φ and of the axioms of T can be chosen so that T + REF0 (φ) proves the consistency of T + REFn ().) In the ca ...
... than an extension by n-reflection, unless the same formula is used to define the axioms of T in both extensions. (This is a consequence of the fact, which will emerge below, that definitions φ and of the axioms of T can be chosen so that T + REF0 (φ) proves the consistency of T + REFn ().) In the ca ...
