Related papers: Invertibility in the mis\`ere multiverse
We investigate finite groups with the Magnus Property, where a group is said to have the Magnus Property (MP) if whenever two elements have the same normal closure then they are conjugate or inverse conjugate. In particular we observe that…
We give an introduction to the cosmological multiverse, aimed at an audience of artists. We discuss general relativity -- our modern theory of gravity -- and the cosmological constant, which is widely believed to be responsible for the…
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture, constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…
The complex (composite) systems such as the Universe allow the different decompositions into subsystems. The Everett's Many Times Interpretation (MWI) heavily relies on the occurrence of decohernce that should provide the classical reality…
The fundamental laws and constants of our universe seem to be finely tuned for life. The various multiverse hypotheses are popular explanations for the fine tuning. This paper reviews the four main suggestions on inference in the presence…
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…
Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means…
This paper offers a synthesis of the positions in the literature regarding controversies about the multiverse. After reviewing some simple elements of modern cosmology and its observational limitations, we will present the history of the…
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…
In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
We examine the condition that a complex Banach algebra $A$ have dense invertible group. We show that, for commutative algebras, this property is preserved by integral extensions. We also investigate the connections with an old problem in…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…