The connection between computability and de nability is one of the main themes in computable mode... more The connection between computability and de nability is one of the main themes in computable model theory. A decidable theory has a decidable model, that is, a model with a decidable elementary diagram. On the other hand, in a computable model only the atomic diagram must be decidable. For some nonisomorphic structures that are elementarily equivalent, we can use computable (in nitary) sentences to describe different structures. In general, if two computable structures satisfy the same computable sentences, then they are isomorphic. Roughly speaking, computable formulas are L!1!-formulas with disjunctions and conjunctions over computably enumerable index sets. Let > 0 be a computable ordinal. A computable ( , resp.) formula is a computably enumerable disjunction (conjunction, resp.) of formulas 9u (x; u) (8u (x; u), resp.) where is computable ( , resp.) for some < . A computable 0 or 0 formula is a nitary quanti er-free formula. To show that our Harizanov was partially suppor...
Journal of Knot Theory and Its Ramifications, 2018
We investigate algebraic and computability-theoretic properties of orderable magmas. A magma is a... more We investigate algebraic and computability-theoretic properties of orderable magmas. A magma is an algebraic structure with a single binary operation. A right order on a magma is a linear ordering of its domain, which is right-invariant with respect to the magma operation. We use tools of computability theory to investigate Turing complexity of orders on computable orderable magmas. A magma is computable if it is finite, or if its domain can be identified with the set of natural numbers and the magma operation is computable. Interesting orderable magmas that are not even associative come from knot theory.
We have now determined the molecular structure of IrIHâ(Hâ)(PPr{sup i}â)â · CââHâ (2·CââHâ) t... more We have now determined the molecular structure of IrIHâ(Hâ)(PPr{sup i}â)â · CââHâ (2·CââHâ) through a single-crystal neutron diffraction study and carried out lNS studies on this complex. We report the result of these studies and their implications on the mechanism of dihydrogen/hydride interchange in the IrXHâ(Hâ)(PPr{sup i}â)â complexes. Our results suggest that the interconversion of dihydrogen and hydride ligands in
The connection between computability and de nability is one of the main themes in computable mode... more The connection between computability and de nability is one of the main themes in computable model theory. A decidable theory has a decidable model, that is, a model with a decidable elementary diagram. On the other hand, in a computable model only the atomic diagram must be decidable. For some nonisomorphic structures that are elementarily equivalent, we can use computable (in nitary) sentences to describe different structures. In general, if two computable structures satisfy the same computable sentences, then they are isomorphic. Roughly speaking, computable formulas are L!1!-formulas with disjunctions and conjunctions over computably enumerable index sets. Let > 0 be a computable ordinal. A computable ( , resp.) formula is a computably enumerable disjunction (conjunction, resp.) of formulas 9u (x; u) (8u (x; u), resp.) where is computable ( , resp.) for some < . A computable 0 or 0 formula is a nitary quanti er-free formula. To show that our Harizanov was partially suppor...
Journal of Knot Theory and Its Ramifications, 2018
We investigate algebraic and computability-theoretic properties of orderable magmas. A magma is a... more We investigate algebraic and computability-theoretic properties of orderable magmas. A magma is an algebraic structure with a single binary operation. A right order on a magma is a linear ordering of its domain, which is right-invariant with respect to the magma operation. We use tools of computability theory to investigate Turing complexity of orders on computable orderable magmas. A magma is computable if it is finite, or if its domain can be identified with the set of natural numbers and the magma operation is computable. Interesting orderable magmas that are not even associative come from knot theory.
We have now determined the molecular structure of IrIHâ(Hâ)(PPr{sup i}â)â · CââHâ (2·CââHâ) t... more We have now determined the molecular structure of IrIHâ(Hâ)(PPr{sup i}â)â · CââHâ (2·CââHâ) through a single-crystal neutron diffraction study and carried out lNS studies on this complex. We report the result of these studies and their implications on the mechanism of dihydrogen/hydride interchange in the IrXHâ(Hâ)(PPr{sup i}â)â complexes. Our results suggest that the interconversion of dihydrogen and hydride ligands in
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