منابع مشابه
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 ...
متن کاملFurther 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...
متن کاملAdvances in Cardinal Arithmetic Sh420
I thank Alice Leonhardt for typing (and retyping) the manuscript so nicely and accurately.
متن کاملCardinal 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,...
متن کاملForcing Axioms and Cardinal Arithmetic
We survey some recent results on the impact of strong forcing axioms such as the Proper Forcing Axiom PFA and Martin’s Maximum MM on cardinal arithmetic. We concentrate on three combinatorial principles which follow from strong forcing axioms: stationary set reflection, Moore’s Mapping Reflection Principle MRP and the P-ideal dichotomy introduced by Abraham and Todorčević which play the key rol...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.2307/1995678