Set existence principles of Shoenfield, Ackermann, and Powell
Set mappings on generalized linear continua
Set theoretic real analysis.
Set theoretical analogues of two combinatorial theorems
Set theories incorporating Hilbert's ε-symbol [Book]
Set theory and category theory: Two rival siblings and their relations with the foundations of mathematics. (La théorie des ensembles et la théorie des catégories: Présentation de deux soeurs ennemies du point de vue de leurs relations avec les fondements des mathématiques.)
Set theory in predicate calculus with equality
Set theory over classes [Book]
Set theory with free construction principles
Set-like equivalence and inner and outer cuts
Sets with no uncountable Blackwell subsets
Set-theoretic characteristics of summability of sequences and convergence of series
Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems [Book]
Set-theoretic constructions of two-point sets
A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice....
Seven characterizations of non-meager 𝖯-filters
We give several topological/combinatorial conditions that, for a filter on ω, are equivalent to being a non-meager -filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager -filter. Here, we identify a filter with a subspace of through characteristic functions. Along the way, we generalize to non-meager -filters a result of Miller (1984) about -points, and we employ and give a new proof of results of Marciszewski (1998). We also employ a theorem...
Several results on set-valued possibilistic distributions
When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...
Sheaf constructions in universal algebra and model theory
Sheaves and concepts : a model-theoretic interpretation of Grothendieck topoi
Shelah's Singular Compactness Theorem.
Shiftings of the horizon