Related papers: Independence of Essential Sets in Finite Implicati…
The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least half of its members. Although the conjecture is known to be…
We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then…
Let $G$ be a finite group. In 2024, Cameron introduced two different concepts of independence (namely independence and strong independence) for the subsets of $G$, yielding to the definition of two simplicial complexes whose vertices are…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
We generalize the notion of essential closures which is used in formulating a geometric necessary condition for a set to be the support of a multivariate copula. Furthermore, in some special cases, we derive an explicit formula of the…
Let A be an asymptotic basis for N_0 of some order. By an essentiality of A one means a subset P such that A\P is no longer an asymptotic basis of any order and such that P is minimal among all subsets of A with this property. A finite…
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
We show that it is consistent relative to ZF, that there is no well-ordering of $\mathbb{R}$ while a wide class of special sets of reals such as Hamel bases, transcendence bases, Vitali sets or Bernstein sets exists. To be more precise, we…
The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set…
Independence of premise principles play an important role in characterizing the modified realizability and the Dialectica interpretations. In this paper we show that a great many intuitionistic set theories are closed under the…
Integrity constraints such as functional dependencies (FD) and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate…
We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The…
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…