Search
Search Results
-
Infinite decreasing chains in the Mitchell order
It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded....
-
Long Borel Games
We study games of length ω 2 with moves in ℕ and Borel payoff. These are, e.g., games in which two players alternate turns playing digits to produce a...
-
Copositive Optimization and Its Applications in Graph Theory
Recently, copositive optimization has received a lot of attention to the Operational Research community, and it is rapidly expanding and becoming a...
-
Model theoretic characterizations of large cardinals
We consider compactness characterizations of large cardinals. Based on results of Benda [Ben78], we study compactness for omitting types in various...
-
Forcing level by level equivalence and a consequence of UA
We show how Hamkins’ Gap Forcing Theorem of Hamkins (Israel J Math 125:237–252, 2001, Bull Symb Logic 5: 264–272, 1999) can be used to give an...
-
Critical cardinals
We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming...
-
Ordinal definable subsets of singular cardinals
A remarkable result by Shelah states that if κ is a singular strong limit cardinal of uncountable cofinality, then there is a subset x of κ such that...
-
-
Square principles in ℙmax extensions
By forcing with P max over strong models of determinacy, we obtain models where different square principles at ω 2 and ω ...
-
I0 and rank-into-rank axioms
This is a survey about I0 and rank-into-rank axioms, with some previously unpublished proofs.
-
Techniques
This chapter will deal in depth with the techniques used in the stonecutting process, from formal definition to actual carving and voussoir...
-
Morasses, semimorasses and supercompact ultrafilters
We prove that morasses are not only compatible with supercompact cardinals, but, moreover, simplified morasses can be elements of the supercompact...
-
PFA and guessing models
This paper explores the consistency strength of The Proper Forcing Axiom (PFA) and the theory (T) which involves a variation of the Viale–Weiβ...
-
Superstrong and other large cardinals are never Laver indestructible
Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank...
-
The structure of the Mitchell order—I
We isolate here a wide class of well-founded orders called tame orders, and show that each such order of cardinality at most κ can be realized as the...