Related papers: Complete Totalities
We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees…
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…
The paper introduces the notion of the size of countable sets that preserves the Part-Whole Principle and generalizes the notion of the cardinality of finite sets. The sizes of natural numbers, integers, rational numbers, and all their…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
We discuss two main ways in comparing and evaluating the size of sets: the "Cantorian" way, grounded on the so called Hume principle (two sets have equal size if they are equipotent), and the "Euclidean" way, maintaining Euclid's principle…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
In this paper, a generalized version of the von Neumann universe known as the total universe is proposed to formally introduce non-well-founded sets that include infinitons, semi-infinitons and quasi-infinitons in Russell's paradox. All…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible…
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
Mathematicians still use Naive Set Theory when generating sets without danger of producing any contradiction. Therefore their working method can be considered as a consistent inference system with an experience of over 100 years. My…
More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case…
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…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…