We consider a two-period pure-exchange economy, where uncertainty prevails and agents, possibly asymmetrically informed, exchange commodities securities of all kinds. Consumers’ characteristics, anticipations, beliefs actions are private typically not known nor assessed by the other agents. This setting drops rational expectations along ‘common knowledge rationality market clearing’ (CKRMC) ass...

Our aim is to present constructions in which some of the cofinalities drop down, i.e. the generators of PCF structure are far a part. 1 Some Preliminary Settings Let λ0 < κ0 < λ1 < κ1 < ... < λn < κn < ...., n < ω be a sequence of cardinals such that for each n < ω • λn is λ +n+2 n +2 n strong as witnessed by an extender Eλn • κn is κ +n+2 n +2 n strong as witnessed by an extender Eκn Let κ = ⋃...

Bird dropping in terminology of stone deterioration pattern is a sub branch of deposit decay, means accumulation of exogenic materials, on stone surface, dropping has a main role in deterioration of buildings and stone monuments. Birds not only to build the nests and noisy cause to bother, but also due to transfer of variety disease into human, especially when it drops any place and then this d...