Related papers: De Finetti for mathematics undergraduates
We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…
This paper gives a complete proof of a theorem of de Bruijn that classifies additive systems for the nonnegative integers, that is, families $\mca = (A_i)_{i\in I}$ of sets of nonnegative integers, each set containing 0, such that every…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
We model voting behaviour in the multi-group setting of a two-tier voting system using sequences of de Finetti measures. Our model is defined by using the de Finetti representation of a probability measure (i.e. as a mixture of…
The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)|size(P))…
This is the text of an expository talk given at the May 1997 Detroit meeting of the American Mathematical Society. It is a tale of a famous football player and a subtle problem he posed about the uniform convergence of Dirichlet series.…
The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
The purpose of this note is to prove the existence of a randomized mechanism, a social decision scheme (SDS), with desirable fairness, efficiency, and strategyproofness properties unmatched by all known SDSs. In particular, we disprove a…
We study stochastic team (known also as decentralized stochastic control or identical interest stochastic dynamic game) problems with large or countably infinite number of decision makers, and characterize existence and structural…
We present a novel analogue for finite exchangeable sequences of the de Finetti, Hewitt and Savage theorem and investigate its implications for multi-marginal optimal transport (MMOT) and Bayesian statistics. If $(Z_1,...,Z_N)$ is a…
We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional…
In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…
A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
G\"odel's first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin's incompleteness theorem and a very…
In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953.…
In this PhD thesis the ancient question of determinism ('Does every event have a cause ?') will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic:…
This is a survey and research note on the modified Orlik conjecture derived from the division theorem introduced in [2]. The division theorem is a generalization of classical addition-deletion theorems for free arrangements. The division…
Cohen's first model is a model of Zermelo--Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of Choice fails. We force over this model to add a function from…
The main motivation for this article is to explore the connections between the existence of certain combinatorial patterns (as in van der Corputs's theorem on arithmetic progressions of length $3$) with well-known tools and theorems for…