Related papers: The grounded Martin's axiom
An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…
Laver, and Woodin independently, showed that models of ${\rm ZFC}$ are uniformly definable in their set-forcing extensions, using a ground model parameter. We investigate ground model definability for models of fragments of ${\rm ZFC}$,…
In this Note we show that the notion of a basis of a finite-dimensional vector space could be introduced by an argument much weaker than Gauss' reduction method. Our aim is to give a short proof of a simply formulated lemma, which in fact…
We show that if one starts with a Universe with some matter and a cosmological constant, then quantum mechanics naturally induces an attractive gravitational potential and an effective Newton's coupling. Thus gravity is an emergent…
Neukirch has developed explicit and axiomatic class field theory, which applies to both local and global fields. One of the key ingredients in his theory is a $\hat{\mathbb{Z}}$-extension of the base field, and in the case of…
The model of a universe with a preferred frame, which nevertheless shares the main properties with traditional special and general relativity theories, is considered. We adopt Mach's interpretation of inertia and show that the energy…
We show that for $\Pi_2$-properties of second or third order arithmetic as formalized in appropriate natural signatures the apparently weaker notion of forcibility overlaps with the standard notion of consistency (assuming large cardinal…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
The accepted idea that the expansion of the universe is accelerating needs, for compatibility to general relativity, the introduction of some unusual forms of matter. However, several authors have proposed that instead of making weird…
We introduce two types of variations of setwise climbability properties, which have been introduced by the second author as fragments of Jensen's square principles. We show that variations of the first type are equivalent to known…
The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from $2$ this theorem is extended here to function…
The search for the physical mechanism underlying the observational evidence for the acceleration of the recent universe is a compelling goal of modern fundamental cosmology. Here we quantitatively study a class of homogeneous and isotropic…
Recently a covariant entropy conjecture has been proposed for dynamical horizons. We apply this conjecture to concordance cosmological models, namely, those cosmological models filled with perfect fluids, in the presence of a positive…
We conjecture that it is not possible to finitely axiomatize matroid representability in monadic second-order logic for matroids, and we describe some partial progress towards this conjecture. We present a collection of sentences in monadic…
Suppose that $T^*$ is an $\omega_1$-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA($T^*$) for proper forcings which preserve these properties of $T^*$. We prove that PFA($T^*$) implies many of the strong…
Some time ago Mbelek and Lachieze-Rey proposed that the discrepancy between the results of the various measurements of Newton's constant could be explained by introducing a gravielectric coupling between the Earth's gravitational and…
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
In this paper, we extend the concept of \( b \)-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results…
The Machian Universe, is usually described with Newtonian Physics, We give an alternative General Relativistic picture for Mach's Universe. As such, we show that, in the correct Machian limit, Schwarzschild's metric is coherent with…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…