相关论文: Strong Compactness and the Ultrapower Axiom
Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…
The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…
We extend and improve the result of Makkai and Par\'e that the powerful image of any accessible functor F is accessible, assuming there exists a sufficiently large strongly compact cardinal. We reduce the required large cardinal assumption…
After small forcing, any < kappa-closed forcing will destroy the supercompactness, even the strong compactness, of kappa .
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
We show that the weakest versions of Foreman's minimal generic hugeness axioms cannot hold simultaneously on adjacent cardinals. Moreover, conventional forcing techniques cannot produce a model of one of these axioms.
We study the structure of the Rudin-Frolik order on countably complete ultrafilters under the assumption that this order is directed. This assumption, called the Ultrapower Axiom, holds in all known canonical inner models. It turns out that…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can possibly exist, unless it yields contradiction" (Possibility…
We establish a comparison principle for viscosity subsolutions and supersolutions of a broad class of second-order quasilinear, maximally subelliptic PDEs on general manifolds. In fact, we prove the comparison theorem for a larger class of…
A revised version of the compactness criterion for families of quantum operations in the strong convergence topology (obtained previously) is presented, along with a more detailed proof and the examples showing the necessity of this…
Rado's Conjecture is a compactness/reflection principle that says any nonspecial tree of height $\omega_1$ has a nonspecial subtree of size $\leq \aleph_1$. Though incompatible with Martin's Axiom, Rado's Conjecture turns out to have many…
We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three…
While many inner model theoretic combinatorial principles are incompatible with large cardinal axioms, on some rare occasions, large cardinals actually imply that the structure of the universe of sets is analogous to the canonical inner…
We force over the constructible universe to obtain a model of the $\Pi^1_3$-reduction property, thus lowering the best known large cardinal strength from the existence of $M_1^{\#}$ to just ZFC. In this model the $\Pi^1_3$-uniformization…
This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups and affine spaces that may be of independent interest.
When a light scalar field with gravitational strength interacts with matter, the weak equivalence principle is in general violated, leading for instance to a violation of the universality of free fall. This has been known and tested for a…
We revisit the classical monotone-follower problem and consider it in a generalized formulation. Our approach is based on a compactness substitute for nondecreasing processes, the Meyer-Zheng weak convergence, and the maximum principle of…
We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a…