We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2κ = κ+, another for which 2κ = κ++ ...

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 introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the "bargaining power" of a group is proportional to cα, where c is the cardinality of the group. Subject classification: JEL C71, C78

Using the concept of m-open sets, M-regularity and M-normality are introduced investigated. Both these notions closed under arbitrary product. M-normal spaces found to satisfy a result similar Urysohn lemma. It is shown that sets can be separated by m-continuous functions in regular space.

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 :...

We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

E. Reznichenko and O. Sipacheva called a space X “FréchetUrysohn for finite sets” if the following holds for each point x ∈ X: whenever P is a collection of finite subsets of X such that every neighborhood of x contains a member of P , then P contains a subfamily that converges to x. We continue their study of this property. We also look at analogous notions obtained by restricting to collectio...