arXiv subjects
Publications and source records attributed to Aleksander Ivanov.
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We consider appropriate algorithmic problems concerning continuous theories of natural classes of these structures.
We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.
We prove that if a Polish G with a comeagre conjugacy class has a non-nesting action on an R-tree, then every element of G fixes a point.
Let G be a closed subgroup of the group of all permutations of a countably infinite set. Let X be a Polish G-space with a countable basis A of clopen sets. Each x from X defines a characteristic function f on A by f(U)=1 iff x belongs to U (where U is from A). We consider computable complexity of f and some related questions.