Related papers: Can Laplace's formula model a deterministic univer…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
It was generally believed throughout the 20-th century that irreversibility is a purely classical event without operator counterpart. However, a classical irreversible system cannot be consistently decomposed into a finite number of…
Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\tau\in[n]$. Classical probabilistic arguments are used to rederive the asymptotic mean, variance and limiting law of $LA_{n}(\tau)$.…
The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different…
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory…
We interpret a formula established by Lapid-M\'{\i}nguez on real regular representations of ${\rm GL}_n$ over a local non-archimedean field as a matrix determinant. We use the Lewis Carroll determinant identity to prove new relations…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definition into a formal mathematical language without inviting…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
It is argued that although quantum theory isn't an absolutely deterministic theory, it is partially deterministic. The approach followed here is in the framework of the standard (Copenhagen interpretation of) quantum mechanics without any…
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…
The theoretical existence of Busy Beaver numbers provides a new notion for decidability and corresponding heuristic for conjectures. The minimum number of states in which a conjecture can be modeled gives a classification of what logic…
We prove that some natural "outside" property is equivalent (for a first order class) to being stable. For a model, being resplendent is a strengthening of being kappa-saturated. Restricting ourselves to the case kappa > |T| for…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…