Related papers: Generalizing Hartogs' Trichotomy Theorem
The paper contains a very simple proof of the classical Hasumi's theorem that each usco mapping defined on an extremally disconnected space has a continuous selection. The paper also contains a very simple proof of a recent result about…
The axioms of ZFC provide a foundation for mathematics, however, there are statements independent of ZFC, such as the Continuum Hypothesis (CH). We discuss Martin's axiom, which is an alternative to CH that roughly states that if there is a…
A conjecture of Thomassen from 1982 states that for every k there is an f(k) so that every strongly f(k)-connected tournament contains k edge-disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament…
Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these…
The paper is a first of two and aims to show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic…
In a sequence of four papers, we prove the following results (via a unified approach) for all sufficiently large $n$: (i) [1-factorization conjecture] Suppose that $n$ is even and $D\geq 2\lceil n/4\rceil -1$. Then every $D$-regular graph…
An assembly of $n$ voters needs to decide on $t$ independent binary issues. Each voter has opinions about the issues, given by a $t$-bit vector. Anscombe's paradox shows that a policy following the majority opinion in each issue may not…
Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…
We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about…
Let $\Theta(G)$ denote the Shannon capacity of a graph $G$. We give an elementary proof of the equivalence, for any graphs $G$ and $H$, of the inequalities $\Theta(G\sqcup H)>\Theta(G)+\Theta(H)$ and $\Theta(G\boxtimes…
We present a new proof that the statement 'every subgroup of a free group is free' implies the Axiom of Choice for finite sets.
We show, in Zermelo-Fraenkel set theory without the Axiom of Choice, that the existence of a discontinuous homomorphism of the additive group of real numbers induces a selector for the Vitali equivalence relation $\mathbb{R}/\mathbb{Q}$.…
We prove that Arhangelskii's problem has a consistent positive answer: if V\models CH, then for some aleph_1-complete aleph_2-c.c. forcing notion P of cardinality aleph_2 we have that P forces ``CH and there is a Lindelof regular…
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…
Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The…
Harvey Friedman, in his remarkable paper Finite functions and the necessary use of large cardinals, Ann. Math. 148:803-893, 1998 and in a technical report, Applications of large cardinals to graph theory, Ohio State University, 1997,…
We study the logical structure of Teichm{\"u}ller-Tukey lemma, a maximality principle equivalent to the axiom of choice and show that it corresponds to the generalisation to arbitrary cardinals of update induction, a well-foundedness…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
The article considers the Choice Axiom.
Paper develops axiomatic characterization of the family of majority vote rules in the way alternative to characterization of the majority vote given in paper of Kenneth O. May in the 1952. This, similar but different, axiomatics focuses on…