Related papers: On the information-theoretic approach to G\"odel's…
We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
The integrated information theory of consciousness (IIT) is uniquely ambitious in proposing a mathematical formula, derived from apparently fundamental properties of conscious experience, to describe the quantity and quality of…
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered.…
In a recent letter (Phys. Lett. A 377 (2013) 1076, arXiv:0905.3801), the authors presented an impossibility proof of quantum bit commitment, which attempted to cover all possible protocols that involve both quantum and classical…
The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the…
G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…
This is a 1971 dissertation. Only its extended abstract was published at the time. While some results appeared in other publications, a number of details remained unpublished and may still have relevance.
In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order arithmetic. This paper questions the…
This thesis addresses the foundational aspects of formal methods for applications in security and in particular in anonymity. More concretely, we develop frameworks for the specification of anonymity properties and propose algorithms for…
We investigate modules over "systematic" rings. Such rings are "almost graded" and have appeared under various names in the literature; they are special cases of the G-systems of Grzeszczuk. We analyse their K-theory in the presence of…
Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…
The First and Second Liouville's Theorems provide correspondingly criterium for integrability of elementary functions "in finite terms" and criterium for solvability of second order linear differential equations by quadratures. The…