相关论文: Cardinal arithmetic for skeptics
This introduction to arithmetic coding is divided in two parts. The first explains how and why arithmetic coding works. We start presenting it in very general terms, so that its simplicity is not lost under layers of implementation details.…
The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…
We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to…
In various situations, decision makers face experts that may provide conflicting advice. This advice may be in the form of probabilistic forecasts over critical future events. We consider a setting where the two forecasters provide their…
Applying Baaz's Generalization Method and a new technique to, respectively, proofs and denumerable simple graphs, diverse arithmetical patterns are observed. In particular, sufficient conditions for a number to be a divisor of a Fermat…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing inductive proof search. In addition, we will show how various…
We investigate the possibilities of global versions of Chang's Conjecture that involve singular cardinals. We show some $\mathrm{ZFC}$ limitations on such principles, and prove relative to large cardinals that Chang's Conjecture can…
We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance…
The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
Recent results of Hindman, Leader and Strauss and of Fern\'andez-Bret\'on and Rinot showed that natural versions of Hindman's Theorem fail {\em for all} uncontable cardinals. On the other hand, Komj\'ath proved a result in the positive…
We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances of the resurrection axioms are equiconsistent over ZFC with the existence of an…
The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…