We prove that for κ an uncountable cardinal, there exist 2κ many non homeomorphic weakly compact convex subsets of weight κ in the Hilbert space l2(κ).

We extend the core model induction technique to a choiceless context, and we exploit it to show that each one of the following two hypotheses individually implies that AD, the Axiom of Determinacy, holds in the L(R) of a generic extension of HOD: (a) ZF + every uncountable cardinal is singular, and (b) ZF + every infinite successor cardinal is weakly compact and every uncountable limit cardinal...

Assume that κ and λ are respectively strong weakly compact cardinals with λ>κ. Fix Θ≥λ a cardinal cof(Θ)>κ cof(δ)=δ<κ. Assuming the GCH≥κ holds, we construct generic extension of universe where is limit cardinal, cof(κ)=δ, 2κ=Θ TP(κ++) holds. This extends main result [5] for uncountable cofinalities.

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

I use generic embeddings induced by generic normal measures on Pκ(λ) that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be used in order to obtain the forcing axioms MA(<μ-closed) in forcing extensions. This has consequences in V: The singular cardinal hypothesis holds above κ, and κ has a useful Jónsson-like property. This, in turn, implies that...

A compact LOTS has an ω 1 -like base if and only if it is metrizable. An infinite cardinal κ is the Noetherian type of a compact LOTS if and only if κ 6= ω1 and κ is not weakly inaccessible. If X is a homogeneous compactum with regular weight, then every base of X contains an Nt(X)op-like

For a cardinal κ and a model M of cardinality κ let No(M) denote the number of non-isomorphic models of cardinality κ which are L∞,κequivalent to M . We prove that for κ a weakly compact cardinal, the question of the possible values of No(M) for models M of cardinality κ is equivalent to the question of the possible numbers of equivalence classes of equivalence relations which are Σ1-definable ...

The Kuznetsov–Index of a modal logic is the least cardinal μ such that any consistent formula has a Kripke–model of size ≤ μ if it has a Kripke–model at all. The Kuznetsov–Spectrum is the set of all Kuznetsov–Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov–Index iω+ω. Futhermore, Chagrov has constructed an extension...

One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. I introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. T...