The Internet Archive has a preservation copy of this work in our general collections.
The file type is `application/pdf`

.

## Filters

##
###
On union ultrafilters
[article]

2011
*
arXiv
*
pre-print

We present some new results on union

arXiv:1012.4532v2
fatcat:twd4cf6alnhohmfqdltqvaffem
*ultrafilters*. We characterize stability for union*ultrafilters*and, as the main result, we*construct*a new kind*of*unordered union*ultrafilter*. ...*of*Berlin. ... Acknowledgments This work evolved out*of*the author's Ph.D. thesis [Kra09] written under the supervision*of*Sabine Koppelberg at the Freie Universität Berlin and supported by the NaFöG grant*of*the state ...##
###
Slow ultrafilters and asymptotic cones of proper metric spaces
[article]

2010
*
arXiv
*
pre-print

Furthermore I answer a question

arXiv:1010.1699v1
fatcat:3h7ujapxijbpvcxivhryfth2ui
*of*Drutu and Sapir concerning slow*ultrafilters*. ... In this paper I present an elementary*construction*to prove that any proper metric space can arise as the asymptotic cone*of*another proper metric space. ... Let α be the*sequence**of*scaling factors obtained by ordering the elements*of*A in the natural order and β the*sequence*obtained*from*the*set*B. ...##
###
Selective ultrafilters and $\omega \rightarrow (\omega )^\omega $

1999
*
Proceedings of the American Mathematical Society
*

Logic. 12 (1977) , 59-111) proved that, assuming the existence

doi:10.1090/s0002-9939-99-04835-2
fatcat:af7xc5hm7ng6zn3o2mq3esgg5y
*of*a Mahlo cardinal, it is consistent that CH holds and every*set**of*reals in L(R) is U-Ramsey with respect to every selective*ultrafilter*... Now we turn to the*construction*. We define for each α < ω 1 the*sequence*Z α = Z ξ : ξ < ω · 2α (3.4) (so Z α+1 is obtained*from*Z α by appending a*sequence**of*order-type ω + ω). ... Such*ultrafilters*do not necessarily exist -in [3] Kunen*constructs*a model*of*ZFC in which there are no selective*ultrafilters*. ...##
###
On Milliken-Taylor Ultrafilters

2011
*
Notre Dame Journal of Formal Logic
*

We show that the Mathias forcing with a Milliken-Taylor

doi:10.1215/00294527-1499345
fatcat:pncmsldelfabjd73js3vfcjezm
*ultrafilter*destroys all Milliken-Taylor*ultrafilters**from*the ground model. ... We show that k-coloured Milliken-Taylor*ultrafilters*have at least k + 1 near coherence classes*of**ultrafilters*in its projection to ω. ... I thank Jordi-López Abad for his question about the number*of*near coherence classes in the core*of*a Milliken-Taylor*ultrafilter*at this special semester. ...##
###
Minimal idempotent ultrafilters and the Auslander-Ellis theorem
[article]

2015
*
arXiv
*
pre-print

We obtain that the existence

arXiv:1305.6530v2
fatcat:t7jrssot4re3rcevejv274tn6e
*of*minimal idempotent*ultrafilters*restricted to countable algebras*of**sets*is equivalent to the Auslander-Ellis theorem (AET) and that the existence*of*minimal idempotent ...*ultrafilters*as higher-order objects is Π^1_2-conservative over a refinement*of*AET. ... To*construct*this object*from*the*sequence*(n i ) one in general needs µ. The*construction*in the proof*of*Lemma 10 can be summed up in the following way. ...##
###
A parametrized diamond principle and union ultrafilters

2018
*
Colloquium Mathematicum
*

As a corollary, this establishes the existence

doi:10.4064/cm7364-10-2017
fatcat:buf4qoxlhbey7pledm5pckddsy
*of*union*ultrafilters*in the iterated Sacks model*of**Set*Theory. ... We prove that this cardinal invariant is small in the iterated Sacks perfect*set*forcing model, and that its corresponding parametrized diamond principle implies the existence*of*union*ultrafilters*. ... Acknowledgments The first author was partially supported by Postdoctoral Fellowship number 275049*from*the Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico. ...##
###
Countably compact topological group topologies on free Abelian groups from selective ultrafilters

2007
*
Topology and its Applications
*

In 1996, Robbie and Svetlichny

doi:10.1016/j.topol.2006.03.028
fatcat:ueqte3swjfcdxge5asrdlugtpy
*constructed*a Wallace semigroup under CH. In the same year, Tomita*constructed*a Wallace semigroup*from*MA countable . ... In this note, we show that the examples*of*Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family*of*selective*ultrafilters*. ... The authors thank the referee for a careful reading*of*the manuscript and for making several suggestions to improve the presentation*of*the article. ...##
###
MODEL-THEORETIC PROPERTIES OF ULTRAFILTERS BUILT BY INDEPENDENT FAMILIES OF FUNCTIONS

2014
*
Journal of Symbolic Logic (JSL)
*

We begin by showing that any flexible regular

doi:10.1017/jsl.2013.28
fatcat:zbxjxmg7irbwponfpxpuqhpube
*ultrafilter*makes the product*of*an unbounded*sequence**of*finite cardinals large, thus saturating any stable theory. ... less than λ) essentially prevents any subsequent*ultrafilter**from*being flexible, thus*from*saturating any nonlow theory. ... a large*set*U*of*κ so that any two < ζ*from*U have the same associated pattern. ...##
###
Gruff ultrafilters

2016
*
Topology and its Applications
*

We investigate the question

doi:10.1016/j.topol.2016.08.012
fatcat:ggrem5nugrafdoj66m2kbzity4
*of*whether Q carries an*ultrafilter*generated by perfect*sets*(such*ultrafilters*were called gruff*ultrafilters*by van Douwen). ... at the end*of*the paper.] ... The authors would like to thank Andreas Blass for some very fruitful discussions, particularly concerning Cohen's paper [5] , as well as for greatly simplifying the proof*of*Lemma 1.2. ...##
###
Social choice with infinite populations: construction of a rule and impossibility results

1997
*
Social Choice and Welfare
*

We provide a simple

doi:10.1007/s003550050067
fatcat:br32u5uh5beofkzxjv4fmhnivy
*construction**of*social choice rules for economies with infinite populations . ... The rules are continuous, Pareto and nondictatorial ; they are*constructed*as limits*of*individual preferences when the limit exists, and otherwise as adequate generalizations . ... Hence we can*construct*a*sequence*zi , converging on y*from*above, everyone satisfying zi p x. ...##
###
Social choice with infinite populations: construction of a rule and impossibility results
[chapter]

1997
*
Topological Social Choice
*

We provide a simple

doi:10.1007/978-3-642-60891-9_10
fatcat:bxxuasmszfethpngtwsqqt6nta
*construction**of*social choice rules for economies with infinite populations . ... The rules are continuous, Pareto and nondictatorial ; they are*constructed*as limits*of*individual preferences when the limit exists, and otherwise as adequate generalizations . ... Hence we can*construct*a*sequence*zi , converging on y*from*above, everyone satisfying zi p x. ...##
###
Iterated asymptotic cones
[article]

2011
*
arXiv
*
pre-print

In this paper we define a class

arXiv:1108.1146v1
fatcat:7hlkzoh3tzhjfbmy2pdiewlzhq
*of*metric spaces which display a wide range*of*behaviors with respect to iterated asymptotic cones, and we use those to*construct*examples within the class*of*groups. ... Iterated asymptotic cones have been used by Druţu and Sapir to*construct*a group with uncountably many pairwise non-homeomorphic asymptotic cones. ... Take X as above*from*Theorem 2.7, using the*sequence*α to define variable and fixed parts. Let G be a group as in Theorem 3.8. Fix an*ultrafilter*µ and*set*C := Cone µ (G, e, α) . ...##
###
Formulating Szemerédi's Theorem in Terms of Ultrafilters
[article]

2012
*
arXiv
*
pre-print

This diploma thesis gives an interpretation

arXiv:1206.0967v1
fatcat:zln2alfuyzfatmswrqr7d7s3w4
*of*Szemerédi's theorem in terms*of**ultrafilters*as well. ... Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long*sequences**of*numbers that have the same color and that ... Back to*ultrafilter**construction*. In a sense, condition 4*from*the*ultrafilter*definition is also a condition*of*maximality. ...##
###
Finite and countable families of algebras of sets

2010
*
Mathematical Research Letters
*

In the formulation

doi:10.4310/mrl.2010.v17.n4.a3
fatcat:spues2soirc7piyopxegy6xn7y
*of*these conditions we use ω-saturated algebras and finite*sequences**of**ultrafilters*on X. 1. The formulation*of*results 1.1. ... As usual, P(M ) denotes the*set**of*all subsets*of*the*set*M . When it is clear*from*the context, we will not state explicitly that a*set*belongs to P(X). ...*sequence**of*ω-cycles. ...##
###
$G_\delta $ and co-meager semifilters

2016
*
Fundamenta Mathematicae
*

The

doi:10.4064/fm182-2-2016
fatcat:gl2gjv5iqzcxtgrk2ch2hx57k4
*ultrafilters*on the partial order ([ω]^ω,⊆^*) are the free*ultrafilters*on ω, which constitute the space ω^*, the Stone-Cech remainder*of*ω. ... Most notably, we will prove that (ω^*,+) contains minimal left ideals that are also weak P-*sets*. ... Acknowledgement The second author would like to thank the members*of*the Prague*Set*Theory seminar for fruitful discussions*of*the topic. ...
« Previous

*Showing results 1 — 15 out of 8,305 results*