Ultra-Countable Functors and Descriptive Group Theory
نویسنده
چکیده
Let Ȳ be a n-dimensional curve. Is it possible to compute topoi? We show that g̃ = 2. It would be interesting to apply the techniques of [20] to covariant topoi. This reduces the results of [20] to an approximation argument.
منابع مشابه
A Computable Functor from Graphs to Fields
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S, there exists a countable field F with the same essential computable-model-theoretic properties as S. Along the way, we develop a new “computable category the...
متن کاملThe Homeomorphism Problem for Countable Topological Spaces
We consider the homeomorphism problem for countable topological spaces and investigate its descriptive complexity as an equivalence relation. It is shown that even for countable metric spaces the homeomorphism problem is strictly more complicated than the isomorphism problem for countable graphs and indeed it is not Borel reducible to any orbit equivalence relation induced by a Borel action of ...
متن کاملHomogeneous Structures
A relational first order structure is homogeneous if every isomorphism between finite substructures extends to an automorphism. Familiar examples of such structures include the rational numbers with the usual order relation, the countable random and so called Rado graph, and many others. Countable homogeneous structures arise as Fraı̈ssé limits of amalgamation classes of finite structures, and h...
متن کاملGroups and Ultra-groups
In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...
متن کاملMartin’s Conjecture, Arithmetic Equivalence, and Countable Borel Equivalence Relations
There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin’s conjecture on Turing invariant functions. This longstanding open problem in recursion theory has connected to many problems in descriptive set theory, particularly in the theory of countable Borel equivalence relations. In this p...
متن کامل