17,428 research outputs found
Topological Ramsey spaces from Fra\"iss\'e classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points
A general method for constructing a new class of topological Ramsey spaces is
presented. Members of such spaces are infinite sequences of products of
Fra\"iss\'e classes of finite relational structures satisfying the Ramsey
property. The Product Ramsey Theorem of Soki\v{c} is extended to equivalence
relations for finite products of structures from Fra\"iss\'e classes of finite
relational structures satisfying the Ramsey property and the Order-Prescribed
Free Amalgamation Property. This is essential to proving Ramsey-classification
theorems for equivalence relations on fronts, generalizing the Pudl\'ak-R\"odl
Theorem to this class of topological Ramsey spaces.
To each topological Ramsey space in this framework corresponds an associated
ultrafilter satisfying some weak partition property. By using the correct
Fra\"iss\'e classes, we construct topological Ramsey spaces which are dense in
the partial orders of Baumgartner and Taylor in \cite{Baumgartner/Taylor78}
generating p-points which are -arrow but not -arrow, and in a partial
order of Blass in \cite{Blass73} producing a diamond shape in the Rudin-Keisler
structure of p-points. Any space in our framework in which blocks are products
of many structures produces ultrafilters with initial Tukey structure
exactly the Boolean algebra . If the number of Fra\"iss\'e
classes on each block grows without bound, then the Tukey types of the p-points
below the space's associated ultrafilter have the structure exactly
. In contrast, the set of isomorphism types of any product
of finitely many Fra\"iss\'e classes of finite relational structures satisfying
the Ramsey property and the OPFAP, partially ordered by embedding, is realized
as the initial Rudin-Keisler structure of some p-point generated by a space
constructed from our template.Comment: 35 pages. Abstract and introduction re-written to make very clear the
main points of the paper. Some typos and a few minor errors have been fixe
Relational symplectic groupoids
This note introduces the construction of relational symplectic groupoids as a
way to integrate every Poisson manifold. Examples are provided and the
equivalence, in the integrable case, with the usual notion of symplectic
groupoid is discussed.Comment: 36 pages, 1 figur
Topological Semantics and Decidability
It is well-known that the basic modal logic of all topological spaces is
. However, the structure of basic modal and hybrid logics of classes of
spaces satisfying various separation axioms was until present unclear. We prove
that modal logics of , and topological spaces coincide and are
S4T_1 spaces coincide.Comment: presentation changes, results about concrete structure adde
Reduced Coproducts of Compact Hausdorff Spaces
By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the reduced coproduct , which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the ultracoproduct can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces
- …