Displaying similar documents to “On saturated ideals and Ρ ϰ λ ”

Weakly normal ideals ou PKl and the singular cardinal hypothesis

Yoshihiro Abe (1993)

Fundamenta Mathematicae

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In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay’s theorem concerning strongly compact cardinals, we show that λ < κ is decided if P κ λ carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.

Rothberger gaps in fragmented ideals

Jörg Brendle, Diego Alejandro Mejía (2014)

Fundamenta Mathematicae

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The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of F σ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even...

Structural properties of ideals

J. E. Baumgartner, A. D. Taylor, S. Wagon

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CONTENTSPreface.............................................................................................. 5Chapter I. Preliminaries................................................................. 61. Notation and terminology.......................................................... 62. Results from the literature......................................................... 93. Definitions and basic properties.............................................. 11Chapter II. Subnormality and...