Related papers: Univalent foundations and the equivalence principl…
In this article, we discuss the question of whether P equals NP, we do not follow the line of research of many researchers, which is to try to find such a problem Q, and the problem Q belongs to the class of NP-complete, if the problem Q is…
In this article we present an axiomatic definition of sets with individuals and a definition of natural numbers and ordinals. We use the axioms pairs, union, power, regularity and separation. We define the equality of sets and of…
Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…
In this paper, we shall compare two metrics in terms of orderly dependence, a notion developed in exponential vector space in the article 'Basis and Dimension of Exponential Vector Space' by Jayeeta Saha and Sandip Jana in Transactions of…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
Let $G$ be a compact group of linear transformations of an Euclidean space $V$. The $G$-invariant $C^\infty$ functions can be expressed as $C^\infty$ functions of a finite basic set of $G$-invariant homogeneous polynomials, called an…
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding…
We address the question whether quantum probes in a gravitational field can be considered as test particles obeying the weak equivalence principle (WEP). A formulation of the WEP is proposed which applies also in the quantum regime, while…
SAT is not in P, is true and provable in a simply consistent extension B' of a first order theory B of computing, with a single finite axiom characterizing a universal Turing machine. Therefore, P is not equal to NP, is true and provable in…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
Word embeddings are commonly obtained as optimizers of a criterion function $f$ of a text corpus, but assessed on word-task performance using a different evaluation function $g$ of the test data. We contend that a possible source of…
We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_\infty$-invariant and concentrated on a single…
We consider the role of the foundation axiom and various anti-foundation axioms in connection with the nature and existence of elementary self-embeddings of the set-theoretic universe.
Quantum mechanics clearly violates the weak equivalence principle (WEP). This implies that quantum mechanics also violates the strong equivalence principle (SEP), as shown in this paper. Therefore a theory of quantum gravity may not be…
The Vop\v{e}nka principle, which asserts that every proper class of first-order structures in a common language admits an elementary embedding between two of its members, is not equivalent over GBC to the first-order Vop\v{e}nka scheme,…
In this paper, we reject commonly accepted views on fundamentality in science, either based on bottom-up construction or top-down reduction to isolate the alleged fundamental entities. We do not introduce any new scientific methodology, but…
The equivalence principle can be tested by precision experiments based on classical and quantum systems, on the ground as well as in space. In many models, these tests are mostly equivalent in their ability to constrain physics beyond the…