Inflammation is the body's response to injury or infection. As early as 2000 years ago, the Roman encyclopaedist Aulus Cornelius Celsus recognised four cardinal signs of this response-redness, heat, swelling and pain; a fifth sign is loss of function.[...].

We show that under certain large cardinal requirements there is a generic extension in which the power function behaves differently on different stationary classes. We achieve this by doing an Easton support iteration of the Radin on extenders forcing.

We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses ideas of Moore from [11] and the notion of a relativized trace function on pairs of ordinals.

Assuming the existence of an inaccessible cardinal, transitive full models of the whole set theory, equipped with a linearly-valued rank function, are constructed. Such models generalize superstructures and provide a global framework for nonstandard mathematics. MSClassification: 03H05, 03C20.

An estimate for the Novak number of a hyperspace with the Vietoris topology is given. As a consequence it is shown that this cardinal function can decrease passing from a space to its hyperspace.

We provide upper and lower bounds in consistency strength for the theories “ZF + ¬ACω + All successor cardinals except successors of uncountable limit cardinals are regular + Every uncountable limit cardinal is singular + The successor of every uncountable limit cardinal is singular of cofinality ω” and “ZF + ¬ACω + All successor cardinals except successors of uncountable limit cardinals are re...

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++ ...

In this paper, we present similarity metrics, which provide a seamless integration of cardinal and non-cardinal similarity measures. We show that cardinal and non-cardinal ways of measuring similarity in case bases are simply instances of the deenition of similarity metrics, and that a single deenition of the maxima of a similarity metric can be applied in both the cardinal and non-cardinal cas...