Scheme representation for first-order logic
... model) can be interpreted as the set of T-model homomorphisms mapping into M. Every formula ϕ(x1 , . . . , xn ) determines a “definable sheaf” [[ϕ]] over the spectrum. Over each model M , the fiber of [[ϕ]] is the definable set stalkM ([[ϕ]]) = ϕM = {a ∈ |M |n | M |= ϕ(a)}. The space [[ϕ]] is topolo ...
... model) can be interpreted as the set of T-model homomorphisms mapping into M. Every formula ϕ(x1 , . . . , xn ) determines a “definable sheaf” [[ϕ]] over the spectrum. Over each model M , the fiber of [[ϕ]] is the definable set stalkM ([[ϕ]]) = ϕM = {a ∈ |M |n | M |= ϕ(a)}. The space [[ϕ]] is topolo ...
Lectures on Groups of Transformations
... by a locally finite family (W1 )i∈I of relatively compact open sets. Let (Vi )i∈I be a covering og G \X such that V̄i ⊂ Wi for every i ∈ I. We now choose, for every i ∈ I, a relatively compact open set Ui in X and a compact set Ai ⊂ U1 such that q(Ui ) = Wi and q(Ai ) = V̄i . Let A = ∪Ai , B = ∪Ui . ...
... by a locally finite family (W1 )i∈I of relatively compact open sets. Let (Vi )i∈I be a covering og G \X such that V̄i ⊂ Wi for every i ∈ I. We now choose, for every i ∈ I, a relatively compact open set Ui in X and a compact set Ai ⊂ U1 such that q(Ui ) = Wi and q(Ai ) = V̄i . Let A = ∪Ai , B = ∪Ui . ...
tale Fundamental Groups
... Notation. Let G be a topological group. Denote by G-Sets the category with objects (X, a) where X is a set (with the discrete topology) and a : G × X → X a continuous action. Because the topology is discrete, this means the stabilizer of any point is open. Morphisms are the obvious ones. Finite-G-Se ...
... Notation. Let G be a topological group. Denote by G-Sets the category with objects (X, a) where X is a set (with the discrete topology) and a : G × X → X a continuous action. Because the topology is discrete, this means the stabilizer of any point is open. Morphisms are the obvious ones. Finite-G-Se ...
GENTLY KILLING S–SPACES 1. Introduction and Notation In
... in which there are neither Q–sets nor locally compact, locally countable, hereditarily normal S–spaces. We provide such a model in this paper. In fact, in our model 2ℵ0 < 2ℵ1 (so in particular there are no Q–sets) and there are no locally compact, first countable S–spaces at all (hence no locally co ...
... in which there are neither Q–sets nor locally compact, locally countable, hereditarily normal S–spaces. We provide such a model in this paper. In fact, in our model 2ℵ0 < 2ℵ1 (so in particular there are no Q–sets) and there are no locally compact, first countable S–spaces at all (hence no locally co ...
