Induced pseudoorders
We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity...
The information boundedness principle requires that the knowledge obtained as a result of an inference process should not have more information than that contained in the consequent of the rule. From this point of view relevancy transformation operators as a generalization of implications are investigated.
This paper deals with the concept of the “size“ or “extent“ of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantities valued probabilities we introduce and discuss information theoretical concepts.
The structures of the fuzzy information theory are focused on the concept of fuzzy entropy, where the individual information of symbols is considered only implicitely. This paper aims to fill this gap and to study the concepts of fuzzy information. Special attention is paid to the typical fuzzy set theoretical paradigma of monotonicity of operations.
We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of , where κ ⊆ X. Suppose μ < κ, , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in which are internally club but not internally approachable.
We call a topological space -compact if every subset of size has a complete accumulation point in it. Let denote the following statement: and there is such that whenever . We show that if holds and the space is both -compact and -compact then is -compact as well. Moreover, from PCF theory we deduce for every singular cardinal . As a corollary we get that a linearly Lindelöf and -compact space is uncountably compact, that is -compact for all uncountable cardinals .