The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On spaces in which a bound on certain cardinal invariants implies closedness”

Borel Tukey morphisms and combinatorial cardinal invariants of the continuum

Samuel Coskey, Tamás Mátrai, Juris Steprāns (2013)

Fundamenta Mathematicae

Similarity:

We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality 𝔭 ≤ 𝔟 does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting...

κ-strong sequences and the existence of generalized independent families

Joanna Jureczko (2017)

Open Mathematics

Similarity:

In this paper we will show some relations between generalized versions of strong sequences introduced by Efimov in 1965 and independent families. We also show some inequalities between cardinal invariants associated with these both notions.

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

Similarity:

We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.

Some Remarks on Tall Cardinals and Failures of GCH

Arthur W. Apter (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We investigate two global GCH patterns which are consistent with the existence of a tall cardinal, and also present some related open questions.

Some applications of Sargsyan's equiconsistency method

Arthur W. Apter (2012)

Fundamenta Mathematicae

Similarity:

We apply techniques due to Sargsyan to reduce the consistency strength of the assumptions used to establish an indestructibility theorem for supercompactness. We then show how these and additional techniques due to Sargsyan may be employed to establish an equiconsistency for a related indestructibility theorem for strongness.

Equimorphism invariants for scattered linear orderings

Antonio Montalbán (2006)

Fundamenta Mathematicae

Similarity:

Two linear orderings are equimorphic if they can be embedded in each other. We define invariants for scattered linear orderings which classify them up to equimorphism. Essentially, these invariants are finite sequences of finite trees with ordinal labels. Also, for each ordinal α, we explicitly describe the finite set of minimal scattered equimorphism types of Hausdorff rank α. We compute the invariants of each of these minimal types..

Link invariants from finite racks

Sam Nelson (2014)

Fundamenta Mathematicae

Similarity:

We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.

A generic theorem in cardinal function inequalities

Alejandro Ramírez-Páramo (2008)

Colloquium Mathematicae

Similarity:

We establish a general technical result, which provides an algorithm to prove cardinal inequalities and relative versions of cardinal inequalities.

Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions

Arthur W. Apter (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We construct a model for the level by level equivalence between strong compactness and supercompactness with an arbitrary large cardinal structure in which the least supercompact cardinal κ has its strong compactness indestructible under κ-directed closed forcing. This is in analogy to and generalizes the author's result in Arch. Math. Logic 46 (2007), but without the restriction that no cardinal is supercompact up to an inaccessible cardinal.