For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of t...

We investigate the existence of strong colorings on successors of singular cardinals. This work continues Section 2 of [1], but now our emphasis is on finding colorings of pairs of ordinals, rather than colorings of finite sets of ordinals.

Abstract This study examines the effects of different intrinsic and extrinsic-to-potential successors’ factors on willingness potential successors family farms to continue training in future. Building socioemotional wealth (SEW) theory a knowledge-based view, we consider (yet students agricultural schools) perspectives, conceptually empirically examine whether they believe factors, namely, thei...

Assuming some large cardinals, a model of ZFC is obtained in which אω+1 carries no Aronszajn trees. It is also shown that if λ is a singular limit of strongly compact cardinals, then λ carries no Aronszajn trees.