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Negative universality results for graphs

S.-D. Friedman, K. Thompson (2010)

Fundamenta Mathematicae

It is shown that in many forcing models there is no universal graph at the successors of regular cardinals. The proof, which is similar to the well-known proof for Cohen forcing, is extended to show that it is consistent to have no universal graph at the successor of a singular cardinal, and in particular at $ℵ_{ω + 1}$ . Previously, little was known about universality at the successors of singulars. Analogous results show it is consistent not just that there is no single graph which embeds the rest, but that...

Nonaccessible filters in measure algebras and functionals on $L^{\infty} (λ) *$

Ryszard Frankiewicz, Grzegorz Plebanek (1994)

Studia Mathematica

Non-dominating ultrafilters

Vera Fischer, Bernhard Irrgang (2010)

Acta Universitatis Carolinae. Mathematica et Physica

Non-Glimm–Effros equivalence relations at second projective level

Vladimir Kanovei (1997)

Fundamenta Mathematicae

A model is presented in which the $Σ_{2}^{1}$ equivalence relation xCy iff L[x]=L[y] of equiconstructibility of reals does not admit a reasonable form of the Glimm-Effros theorem. The model is a kind of iterated Sacks generic extension of the constructible model, but with an “ill“founded “length” of the iteration. In another model of this type, we get an example of a $Π_{2}^{1}$ non-Glimm-Effros equivalence relation on reals. As a more elementary application of the technique of “ill“founded Sacks iterations, we obtain...

Non-isomorphic Hyper-real Fields from Non-isomorphic Ultrapowers.

Judy Roitman (1982)

Mathematische Zeitschrift

Nonreflecting stationary subsets of $P_{κ} λ$

Yoshihiro Abe (2000)

Fundamenta Mathematicae

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.

Normal restrictions of the noncofinal ideal on $P_{κ} (λ)$

Pierre Matet (2013)

Fundamenta Mathematicae

We discuss the problem of whether there exists a restriction of the noncofinal ideal on $P_{κ} (λ)$ that is normal.

Note on connections of the point of continuity property and Kuratowski problem on function having the Baire property

Ondřej F. K. Kalenda (1997)

Acta Universitatis Carolinae. Mathematica et Physica

Novak's result by Henkin's method

H. Doest (1969)

Fundamenta Mathematicae

Nowhere dense subsets and Booth's Lemma

Viacheslav I. Malykhin (1996)

Commentationes Mathematicae Universitatis Carolinae

The following statement is proved to be independent from $[LB + \neg CH]$ : $(*)$ Let $X$ be a Tychonoff space with $c (X) \leq ℵ_{0}$ and $π w (X) < ℭ$ . Then a union of less than $ℭ$ of nowhere dense subsets of $X$ is a union of not greater than $π w (X)$ of nowhere dense subsets.

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