We show that under the axiom there is no uniformly completely Ramsey null set of size . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.
We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notion of weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees. ...
Axiomatická metoda je považována za hlavní metodu, kterou je dnes matematika formalizována. Není však jedinou, navíc prošla v průběhu tisíciletí poměrně pestrým vývojem. V tomto příspěvku se pokusíme na základě charakterizace různých typů formalizace matematiky zařadit nejznámější pokusy o axiomatizaci eukleidovské geometrie, zejména Eukleidův, Hilbertův a Birkhoffův.
In this note we characterize bipartite MV-algebras by introducing the notion of preboolean MV-algebras.
We consider prediction problems in which each of a countably infinite set of agents tries to guess his own hat color based on the colors of the hats worn by the agents he can see, where who can see whom is specified by a graph V on ω. Our interest is in the case in which 𝓤 is an ultrafilter on the set of agents, and we seek conditions on 𝓤 and V ensuring the existence of a strategy such that the set of agents guessing correctly is of 𝓤-measure one. A natural necessary condition is the absence...