We show that the theories “ZFC + There is a supercompact cardinal” and “ZFC + There is a supercompact cardinal + Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.

My research lies mostly in logic and set theory, and in applications of set-theoretic tools to other areas of mathematics, such as graph theory, algebra, and topology. My set-theoretic work is largely combinatorial in nature and comes in one of two flavors: ZFC results and independence results. ZFC stands for Zermelo-Fraenkel axioms with choice and is the standard set of axioms in which set the...

It is proved that any countable topological group in which the filter of neighborhoods identity element not rapid contains a discrete set with precisely one nonisolated point. This gives negative answer to Protasov's question on existence ZFC nondiscrete all subsets are closed. also extremally disconnected implies ultrafilter and, hence, cannot be constructed ZFC.

A noteworthy feature of general topology – as contrasted with geometry, number theory, and most other fields of mathematics – is that many of its fundamental questions are not decided by " the usual axioms of set theory ". What this means is that if one codifies the set-theoretic assumptions used implicitly in ordinary mathematics and consolidates these in a list of axioms – the usual axioms of...

Nonlinear transport in the low-temperature vortex glass state of single crystal Bi2Sr2CaCu2O8 has been investigated with fast current pulses driven along the ab plane. Field cooled preparation shows a higher threshold current ~marking a jump or break in slope in the voltage response! than the zero field cooled ~ZFC! one, but it is found to be metastable and convertible to the ZFC response by a ...