Displaying similar documents to “A note on infinite forcing.”

On what I do not understand (and have something to say): Part I

Saharon Shelah (2000)

Fundamenta Mathematicae

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This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history...

Some variations on the partition property for normal ultrafilters on Pkl

Julius Barbanel (1993)

Fundamenta Mathematicae

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Suppose κ is a supercompact cardinal and λ≥κ. In [3], we studied the relationship between the weak partition property and the partition property for normal ultrafilters on P κ λ . In this paper we study a hierarchy of properties intermediate between the weak partition property and the partition property. Given appropriate large cardinal assumptions, we show that these properties are not all equivalent.

Compactness and Löwenheim-Skolem properties in categories of pre-institutions

Antonino Salibra, Giuseppe Scollo (1993)

Banach Center Publications

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The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented...

Construction of sentences with specific interpretability properties

A. Stern (1993)

Fundamenta Mathematicae

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The Rowland Institute for Science, 100 Cambridge Parkway, Cambridge, Massachusetts 02142, U.S.A. A construction is presented for generating sentences that satisfy a recursively enumerable set of interpretability properties. This construction is then used to prove three previously announced results concerning the lattice of local interpretability types of theories (also known as the Lattice of Chapters).

Embedding Cohen algebras using pcf theory

Saharon Shelah (2000)

Fundamenta Mathematicae

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Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on ν + .

Nonreflecting stationary subsets of P κ λ

Yoshihiro Abe (2000)

Fundamenta Mathematicae

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We explore the possibility of forcing nonreflecting stationary sets of P κ λ . We also present a P κ λ generalization of Kanamori’s weakly normal filters, which induces stationary reflection.

On a problem of Steve Kalikow

Saharon Shelah (2000)

Fundamenta Mathematicae

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The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for ℵ ω but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants. ...

Weak variants of Martin's Axiom

J. Barnett (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...