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Easton functions and supercompactness

Brent Cody, Sy-David Friedman, Radek Honzik (2014)

Fundamenta Mathematicae

Suppose that κ is λ-supercompact witnessed by an elementary embedding j: V → M with critical point κ, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton’s theorem: (1) ∀α α < cf(F(α)), and (2) α < β ⇒ F(α) ≤ F(β). We address the question: assuming GCH, what additional assumptions are necessary on j and F if one wants to be able to force the continuum function to agree with F globally, while preserving...

Effective decomposition of σ-continuous Borel functions

Gabriel Debs (2014)

Fundamenta Mathematicae

We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering ( A ₙ ) n ∈ ω of X such that f | A ₙ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.

El problema del árbol minimal para grafos difusos.

Miguel Delgado, José Luis Verdegay, M.ª Amparo Vila (1987)

Trabajos de Investigación Operativa

Basándonos en algunas definiciones previas, se analiza el problema del árbol generador difuso. En primer lugar se trata su existencia y después se encuentra el árbol generador difuso de mínimo costo mediante una descomposición por α-cortes. El estudio se realiza para dos estructuras diferentes de costos.

Éléments pour l'étude de relations localement définies («infra-relations»). Infra-ordres et relation ternaire d'intermédiarité

H. Durup (1970)

Mathématiques et Sciences Humaines

Dans les sciences de la nature, et en particulier dans les sciences du comportement, on rencontre fréquemment des relations caractérisées par des propriétés locales. Une famille très vaste de telles relations rassemble celles qui sont définies uniquement par des propriétés portant sur les ensembles d'éléments liés à un même élément, soit par la relation («points vus d'un même point»), soit par son inverse («points d'où l'on voit un même point»). A tout type de relation correspondent ainsi plusieurs...

Embedding Cohen algebras using pcf theory

Saharon Shelah (2000)

Fundamenta Mathematicae

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 + .

Embedding orders into the cardinals with D C κ

Asaf Karagila (2014)

Fundamenta Mathematicae

Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of Z F + D C < κ for any regular κ. We use this theorem to show that for all κ, the assumption of D C κ does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use...

Embedding partially ordered sets into ω ω

Ilijas Farah (1996)

Fundamenta Mathematicae

We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion H E which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

Embeddings into 𝓟(ℕ)/fin and extension of automorphisms

A. Bella, A. Dow, K. P. Hart, M. Hrusak, J. van Mill, P. Ursino (2002)

Fundamenta Mathematicae

Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

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