We discuss a model, in which two agents may distribute finitely many objects among themselves. The conflict is resolved by means of a market procedure. Depending on the specifications, this procedure serves to implement bargaining solutions such as the discrete Raiffa solution, the Kalai-Smorodinsky solution and the Perles-Maschler solution. The latter is axiomatized using the superadditivity a...

We give an affirmative answer to Brendle’s and Hrušák’s question of whether the club principle together with h > א1 is consistent. We work with a class of axiom A forcings with countable conditions such that q ≥n p is determined by finitely many elements in the conditions p and q and that all strengthenings of a condition are subsets, and replace many names by actual sets. There are two types o...

Proof. Without loss of generality, we only need to prove for the case s= 1, as ρ satisfies Axioms A1-A5 if and only if 1 s ρ satisfies Axioms A1-A5 (with s= 1 in Axiom A3). The “only if” part. First, we show that (2) holds for any X ∈L∞(Ω,F , P ). Define the set function ν(E) := ρ(1E),E ∈F . Then, it follows from Axiom A2 and A3 that ν is monotonic, ν(∅) = 0, and ν(Ω) = 1. ForM ≥ 1, define LM :...

Strongly Unfoldable Cardinals Made Indestructible by Thomas A. Johnstone Advisor: Joel David Hamkins I provide indestructibility results for weakly compact, indescribable and strongly unfoldable cardinals. In order to make these large cardinals indestructible, I assume the existence of a strongly unfoldable cardinal κ, which is a hypothesis consistent with V = L. The main result shows that any ...

In this paper, we present a hypergraph-based inference method for conditional independence. Our method allows us to obtain several interesting results on graph combination. In particular, our hypergraph approach allows us to strengthen one result obtained in a conventional graph-based approach. We also introduce a new inference axiom, called combination, of which the contraction axiom is a spec...

1 Three Axioms for a Determinant Function Let d be a scalar-valued function on the space Mn×n of all n×n matrices. Let A1, A2, . . . , An be the n rows of an n×n matrix A. We will denote the value d(A) of A under the function d as d(A) = d(A1, A2, . . . , An), indicating that d is a scalar-valued function of n n-dimensional row vectors A1, A2, . . . , An. The scalar-valued function d is called ...

This paper describes the design, implementation, and testing of a system for selecting necessary axioms from a large set also containing superfluous axioms, to obtain a proof of a conjecture. The selection is determined by semantics of the axioms and conjecture, ordered heuristically by a syntactic relevance measure. The system is able to solve many problems that cannot be solved alone by the u...