Related papers: Reflective Cardinals
People can refer to quantities in a visual scene by using either exact cardinals (e.g. one, two, three) or natural language quantifiers (e.g. few, most, all). In humans, these two processes underlie fairly different cognitive and neural…
We review the discovery of reflection positivity. We also explain a new geometric approach and proof of the reflection positivity property.
In this paper we introduce a new hierarchy of large cardinals between I3 and I2, the iterability hierarchy, and we prove that every step of it strongly implies the ones below.
The central focus is on clarifying the distinction between sets and proper classes. To this end we identify several categories of concepts (surveyable, definite, indefinite), and we attribute the classical set theoretic paradoxes to a…
Despite being an established notion in the large cardinal hierarchy, results about Woodin cardinals are sparse in the literature. Here we gather known results about the preservation of Woodin cardinals under certain forcing extensions, as…
The notions of real and user cardinality of a sign are introduced. Rank distributions can be extended to arbitrary sign objects, i.e., semiotic systems. The dynamics of the distribution of consumer durables, such as automobiles, is studied.
This is an informal introduction to the concept of reflexive polyhedra and some of their most important applications in perturbative and non-perturbative string physics. Following the historical development, topics like mirror symmetry,…
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties, on the other hand, are examples of anti-guessing principles. We discuss the tension and the…
There is an optimal way to increase certain cardinal invariants of the continuum.
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
We define a class of rational numbers including, as a particular case, the classical harmonic numbers. For one particular instance we apply it to the expansion into powers series of a special function, and also detail its relashionship with…
This paper describes problems concerning the range of cardinalities of sumsets and restricted sumsets of finite subsets of the integers and finite subsets of ordered abelian groups.
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
A trick to obtain a systematic solution to the set-theoretical reflection equation is presented from a known one to the Yang-Baxter equation. Examples are given from crystals and geometric crystals associated to the quantum affine algebra…
In the context of large cardinals, the classical diamond principle Diamond_kappa is easily strengthened in natural ways. When kappa is a measurable cardinal, for example, one might ask that a Diamond_kappa sequence anticipate every subset…
A cardinal is weakly Reinhardt if it is the critical point of an elementary embedding from the universe of sets into a model that contains the double powerset of every ordinal. This note establishes the equiconsistency of a proper class of…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called…
Much of the theory of large cardinals beyond a measurable cardinal concerns the structure of elementary embeddings of the universe of sets into inner models. This paper seeks to answer the question of whether the inner model uniquely…
We define complete Segal objects, which play the role of internal higher category objects. Then we study them using representable Cartesian fibrations, in particular defining adjunctions and limits of complete Segal objects. Finally we use…