Menas' Result is Best Possible

Result is Best Possible ” by Arthur

Generalizing some earlier techniques due to the second author, we show that Menas’ theorem which states that the least cardinal κ which is a measurable limit of supercompact or strongly compact cardinals is strongly compact but not 2 supercompact is best possible. Using these same techniques, we also extend and give a new proof of a theorem of Woodin and extend and give a new proof of an unpubl...

The Partition Property for Certain Extendible Measures on Supercompact Cardinals

We give an alternate characterization of a combinatorial property of measures on pKX introduced by Menas. We use this characterization to prove that if k is supercompact, then all measures on pKX in a certain class have the partition property. This result is applied to obtain a self-contained proof that if k is supercompact and X is the least measurable cardinal greater than k, then Solovay's "...

Contrasting the 2007 and 2005 Hurricane Seasons: Evidence of Possible Impacts of Saharan Dry Air and Dust on Tropical Cyclone Activity in the Atlantic Basin

Theories and the Phenomenological Information

The concepts of effective theories in science and of primary theory are reconsidered in the light of the integrative (structural-phenomenological) model of reality. It is shown that the structural effective theories are viable for scales from the universe down to the Planck scale, but not for the deep domain of reality below Planck scale, neither for the domain of all the different universes of...

Scaling in Cosmology and the Arrow of Time

A new type of scaling applicable to a variety of physical parameters in the universe is proposed here. This utilizes a relation linking the fundamental masses and fundamental constants in nature and an axiomatic approach is developed for the relations between microscopic and macroscopic found by Eddington and Dirac. In this approach, the fundamental constants are changing with time and the vari...