Related papers: An $\mathrm{NSOP}_{1}$ theory without the existenc…
Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate version of no-hidden-variables theorem. We derive a proposition concerning the quantum theory under the existence of the Bloch sphere in a single spin-1/2 system.…
An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from non-singular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface…
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
Librationist set theory \pounds ${}$ is developed. It descends from semantics for truth, initiated by Kripke, and others. # extends \pounds, of Librationist closures of the paradoxes in Logic and Logical Philosophy 21(4), 323-361, 2012.…
The main aim of this work is to show, in the absence of the Axiom of Choice, fundamental results on $\mathbf{E}$-compact extensions of $\mathbf{E}$-completely regular spaces, in particular, on Hewitt realcompactifications and Banaschewski…
The formulation of quantum theory does not comply with the notion of objective existence of elementary particles. Objective existence independent of observation implies the distinguishability of elementary particles. In other words: If…
We formulate and discuss a general axiomatic theory of arbitrary objects. This theory is expressed in a simple first-order language without modal operators, and it is governed by classical logic.
We exposit two previously unpublished theorems of Leo Harrington. The first theorem says that there exist arithmetical singletons which are arithmetically incomparable. The second theorem says that there exists a ranked point which is not…
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption…
Archimedean copulas are a popular type of copulas in which a variant of the Archimedean axiom apply. We provide a topological proof of the Archimedean Axiom which is applicable for non-continuous distribution functions.
We discuss some physical consequences of what might be called ``the ultimate ensemble theory'', where not only worlds corresponding to say different sets of initial data or different physical constants are considered equally real, but also…
The possibility of a fundamental consistency between the basic quantum principles and reduction (so-called wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as…
The no-signaling principle in quantum mechanics is shown to be a consequence of Gleason non-contextuality and the tensor product structure.
We give an example of an NIP theory $T$ in which there is a formula that does not fork over $\varnothing$ but has measure $0$ under any global $\varnothing$-invariant Keisler measure, and we show that this cannot occur if $T$ is also…
This paper is devoted to the theoretical analysis of the nonlinear plate equations in $\mathbb{R}^{n}\times (0,\infty),$ $n\geq1,$ with nonlinearity involving a type polynomial behavior. We prove the existence and uniqueness of global mild…
A version of the vacuum conservation theorem is proved which does not assume the existence of a time function nor demands stronger properties than the dominant energy condition. However, it is shown that a stronger stable version plays a…
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…
We consider the dynamics of the classical $SU(2)$ Wu-Yang monopole problem and show a set of new directions for its analysis starting from a variational setting. This allows us to give a new interpretation of the monopole charge as a string…
While the relation between visualization and scientific understanding has been a topic of long-standing discussion, recent developments in physics have pushed the boundaries of this debate to new and still unexplored realms. For it is…