On successors in cardinal arithmetic

More on Cardinal Arithmetic Sh410

Cardinal Arithmetic for Skeptics

When modern set theory is applied to conventional mathematical problems, it has a disconcerting tendency to produce independence results rather than theorems in the usual sense. The resulting preoccupation with “consistency” rather than “truth” may be felt to give the subject an air of unreality. Even elementary questions about the basic arithmetical operations of exponentiation in the context ...

Further Cardinal Arithmetic

We continue the investigations in the author’s book on cardinal arithmetic, assuming some knowledge of it. We deal with the cofinality of (S≤א0 (κ),⊆) for κ real valued measurable (Section 3), densities of box products (Section 5,3), prove the equality cov(λ, λ, θ+, 2) = pp(λ) in more cases even when cf(λ) = א0 (Section 1), deal with bounds of pp(λ) for λ limit of inaccessible (Section 4) and g...

Advances in Cardinal Arithmetic Sh420

I thank Alice Leonhardt for typing (and retyping) the manuscript so nicely and accurately.

Cardinal Arithmetic in Weak Theories

In this paper we develop the theory of cardinals in the theory COPY. This is the theory of two total, jointly injective binary predicates in a second order version, where we may quantify over binary relations. The only second order axioms of the theory are the axiom asserting the existence of an empty relation and the adjunction axiom, which says that we may enrich any relation R with a pair x,...