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The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah.
One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natur...
Conditions one might impose on fair allocation procedures are introduced. Nondiscrimination requires that agents share an item in proportion to their entitlements if they receive nothing else. The "pr...
McMullen's g-vector is important for simple convex polytopes. This paper postulates axioms for its extension to general convex polytopes. It also conjectures that, for each dimension d, a stated fini...
Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,...
We investigate the dynamics of pairs of Fermions and Bosons released from a box and find that their populations have unique generic properties ensuing from the axioms of quantum statistics and symmetr...
In this note, we introduce the degree to which an I-fuzzy topological space (X, τ) is Sub T1 (in short, ST1), which we denote by ST1(X, τ) and proved that KT1(X, τ), defined by Yue and Fang and ST1(X,...
By basing Bayesian probability theory on five axioms, we can give a trivial proof of Cox’s Theorem on the product rule and sum rule for conditional plausibility without assuming...

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