相关论文: The Definability of Fields

This paper aims to show that a simple framework, utilizing basic formalisms from set theory and category theory, can clarify and inform our theories of the relation between mind and matter.

An accurate description of nuclear matter starting from free-space nuclear forces has been an elusive goal. The complexity of the system makes approximations inevitable, so the challenge is to find a consistent truncation scheme with…

Determinism and indeterminism in physical theories are reviewed and some broader implications of determinism are discussed.

We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…

It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different…

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…

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…

The estimation of the electric field in simple situations provides an opportunity to develop intuition about the models used in physics. We propose an activity aimed at university students of General Physics where the electric field of a…

Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…

In this expository article, the real numbers are defined as infinite decimals. After defining an ordering relation and the arithmetic operations, it is shown that the set of real numbers is a complete ordered field. It is further shown that…

In this note, we present a characterization of sets definable in Skolem arithmetic, i.e., the first-order theory of natural numbers with multiplication. This characterization allows us to prove the decidability of the theory. The idea is…

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…

The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…

In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any…

An interesting example of the deep interrelation between Physics and Mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments…

In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…

Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…

We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…

Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…

We follow some (wild) speculations on trying to understand the uniqueness of our physical world, from the field concept to F-Theory.