Remarks on σ-fields without continuous measures
Representability of concrete categories by non-constant morphisms
Representation Theorem for Minimal -Algebras
Rigid Boolean Algebras
Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns
We provide upper and lower bounds in consistency strength for the theories “ZF + + 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 + + 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...
Second order forcing, algebraically closed structures, and large cardinals
Semiproper ideals
We say that an ideal I on is semiproper if the corresponding poset is semiproper. In this paper we investigate properties of semiproper ideals on .
Sequentially continuous mappings of product spaces
Set existence principles of Shoenfield, Ackermann, and Powell
Singular cardinals and strong extenders
We investigate the circumstances under which there exist a singular cardinal µ and a short (κ,µ)-extender E witnessing “κ is µ-strong”, such that µ is singular in Ult(V, E).
Singular Failures of GCH and Level by Level Equivalence
We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is an unbounded set of singular cardinals which witness the only failures of GCH in the universe. In this model, the structure of the class of supercompact cardinals can be arbitrary.
Skeletons, bodies and generalized -algebras
Slender modules, endo-slender abelian groups and large cardinals
Some algebraic properties of weakly compact and compact cardinals
Some applications of Sargsyan's equiconsistency method
We apply techniques due to Sargsyan to reduce the consistency strength of the assumptions used to establish an indestructibility theorem for supercompactness. We then show how these and additional techniques due to Sargsyan may be employed to establish an equiconsistency for a related indestructibility theorem for strongness.
Some combinatorial properties of ultrafilters
Some combinatorics involving ultrafilters
Some operations related with translation
Some properties of stationary sets [Book]
Some remarks on selectors