We introduce a matching model in which agents engage in joint ventures via multilateral contracts. This approach allows us to consider production complementarities previously outs...
Some errors in our original paper in defining relative reduct with information measures are pointed out in this paper. It is shown that in our original work, Theorems 10 and 19 hol...
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theor...
A subgraph H of a graph G is gated if for every x V(G) there exists a vertex u in H such that dG (x, v) = dG (x, u) + d G (u, v) for any v V(H). The gated amalgam of graphs G 1 an...
We show that several known theorems on graphs and digraphs are equivalent. The list of equivalent theorems include Kotzig's result on graphs with unique 1-factors, a lemma by...
Mathematics is facing a dilemma at its heart: the nature of mathematical proof. We have known since Church and Turing independently showed that mathematical provability was undeci...
Abstract. In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can...
We review the past ten years in computational complexity theory by focusing on ten theorems that the author enjoyed the most. We use each of the theorems as a springboard to discus...
Abstract. The relationship between theorems and lemmas in mathematical reasoning is often vague. No system exists that formalizes the structure of theorems in a mathematical librar...
This paper provides a set-theoretic model of knowledge and unawareness, in which reasoning through theorems is employed. A new property called Awareness Leads to Knowledge shows t...