A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Hechler's theorem for the null ideal

2004
*
Archive for Mathematical Logic
*

This is a variation of

doi:10.1007/s00153-004-0224-4
fatcat:75ewvgzoerfw3ftpmjwx3w6kme
*Hechler's*classical result in*the*theory of forcing, and*the*statement of*the**theorem**for**the*meager*ideal*has been already proved by Bartoszynski and*the*author. ... is a basis of*the**null**ideal*of*the*real line which is order-isomorphic to Q with respect to set-inclusion. ... Acknowledgement*The*author would like to thank Tomek Bartoszyński, Jörg Brendle, Shizuo Kamo and Teruyuki Yorioka*for*helpful suggestion and discussion concerning this work. ...##
###
Hechler's theorem for the meager ideal
[article]

2003
*
arXiv
*
pre-print

We prove

arXiv:math/0209086v2
fatcat:2r2irhkvrbd2dkwaz7q4tkfx4e
*the*following*theorem*:*For*a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in*the*forcing model, there ... This is a variation of*Hechler's*classical result in*the*theory of forcing. ... Acknowledgement*The*second author would like to thank Prof. Jörg Brendle and Mr. Teruyuki Yorioka*for*helpful discussion concerning this work. ...##
###
Hechler's theorem for the meager ideal

2005
*
Topology and its Applications
*

We prove

doi:10.1016/j.topol.2003.08.028
fatcat:l2ryg53difcobfk5v5qx34wo7i
*the*following*theorem*:*For*a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in*the*forcing model, there ... This is a variation of*Hechler's*classical result in*the*theory of forcing. ... Acknowledgement*The*second author would like to thank Prof. Jörg Brendle and Mr. Teruyuki Yorioka*for*helpful discussion concerning this work. ...##
###
Higher Dimensional Cardinal Characteristics for Sets of Functions
[article]

2021
*
arXiv
*
pre-print

Finally, using variations of Cohen, Hechler, and localization forcing I prove a number of consistency results

arXiv:1909.07458v2
fatcat:5aalqi6zzjecxnidgx3c4rbbgi
*for*possible values of*the*new cardinals. ... These 18 form two separate diagrams consisting of 6 and 12 cardinals respectively, each resembling versions of*the*Cichoń diagram. These ZFC-inequalities are*the*first main result of*the*paper. ... Finally*the*author would like to thank*the*Austrian Science Fund (FWF)*for**the*generous support through grant number Y1012-N35. ...##
###
Simple Cardinal Characteristics of the Continuum

1994
*
arXiv
*
pre-print

We also discuss some characteristics associated with partition

arXiv:math/9405202v1
fatcat:yes2yedjkfdelg6rf5josfqoiy
*theorems*and we present, in an appendix, a simplified proof of Shelah's*theorem*that*the*dominating number is less than or equal to*the*independence ... We classify many cardinal characteristics of*the*continuum according to*the*complexity, in*the*sense of descriptive set theory, of their definitions. ... Specifically, if we replace*the**ideal*L of measure zero sets by such that*the*relation y ∈ S x is Π 0 2 (or even Π 0 2 in x*for*each fixed y) then unif*for*this*ideal*is ≥ cov(B). ...##
###
Filter-linkedness and its effect on preservation of cardinal characteristics

2020
*
Annals of Pure and Applied Logic
*

This is applied to prove consistency results about Cichoń's diagram (without using large cardinals) and to prove

doi:10.1016/j.apal.2020.102856
fatcat:7q4ugdcsq5ckvjs4lgp27sdmiy
*the*consistency of*the*fact that,*for*each Yorioka*ideal*,*the*four cardinal invariants associated ... Although*Theorems*B, D, E and F are covered by this new result, our methods are different, and in particular*Theorem*B may be useful as a starting point*for*further separation results*for*Cichoń's diagram ... Acknowledgements*The*first author was partially supported by Grants-in-Aid*for*Scientific Research (C) 15K04977 and 18K03398, Japan Society*for**the*Promotion of Science;*the*second author was supported ...##
###
Filter-linkedness and its effect on preservation of cardinal characteristics
[article]

2018
*
arXiv
*
pre-print

This is applied to prove new consistency results about Cichoń's diagram (without using large cardinals) and to prove

arXiv:1809.05004v1
fatcat:tlynuhlelrdufil4iwpbshoyqq
*the*consistency of*the*fact that,*for*each Yorioka*ideal*,*the*four cardinal invariants ... We introduce*the*property "F-linked" of subsets of posets*for*a given free filter F on*the*natural numbers, and define*the*properties "μ-F-linked" and "θ-F-Knaster"*for*posets in*the*natural way. ... We include*the*proof*for*completeness. Property (a) follows from Lemma 5.8(a). To see property (b), let {ċ(α) : α < θ} be a strongly θ-R-unbounded family added by P. ...##
###
Halfway New Cardinal Characteristics
[article]

2018
*
arXiv
*
pre-print

Based on

arXiv:1808.02442v2
fatcat:jzovydvxv5h6pid2qjetuz2iqa
*the*well-known cardinal characteristics s, r and i, we introduce nine related cardinal characteristics by using*the*notion of asymptotic density to characterise different intersection properties ... We prove several bounds and consistency results, e. g.*the*consistency of s < s_1/2 and s_1/2 < non(N), as well as several results about possible values of i_1/2. ... We are grateful to Barnabás Farkas, Martin Goldstern and Salome Schumacher*for*numerous helpful discussions and suggestions. 1 •*the**ideal*N := {A ⊆ 2 ω | λ(A) = 0} of Lebesgue*null*sets and •*the**ideal*...##
###
Alternative Cichoń Diagrams and Forcing Axioms Compatible with CH
[article]

2020
*
arXiv
*
pre-print

I prove iteration and preservation

arXiv:2008.04900v1
fatcat:enltkdvklnfdlhp3wv4x57iaj4
*theorems**for*both classes and use these to produce many new models of*the*subcomplete forcing axiom. ... As an application I investigate in detail*the*Cichoń diagram*for*degrees of constructibility relative to a fixed inner model of ZFC. ...*The*symbols N , M, K denote*the**null**ideal*,*the*meager*ideal*and*the**ideal*generated by σ-compact subsets of ω ω respectively. ...##
###
Coherent systems of finite support iterations
[article]

2017
*
arXiv
*
pre-print

Furthermore, we show that this constellation of 7 values is consistent with

arXiv:1609.05433v2
fatcat:rcitiqcs45gplgz5fngpozqwyi
*the*existence of a Δ^1_3 well-order of*the*reals. ... We use them to produce models of new constellations in Cichoń's diagram, in particular, a model where*the*diagram can be separated into 7 different values. ... We should point out though, that if we are to construct a 3D-system*for**the*above constellation, in order to increase s, we have to include in*the*construction, non-definable, ccc posets which adjoin non-restricted ...##
###
Mazur spaces

1981
*
International Journal of Mathematics and Mathematical Sciences
*

This leads to a new classification of compactT2spacesH, those

doi:10.1155/s0161171281000021
fatcat:ydowxbs6qra5fijrz2dzqpwyky
*for*which*the*weak*dual ofC(H)is a Mazur space. ... space, and whenXis*the*weak*dual of a locally convex space. ... Namely, in standard*Hechler's*model h = ℵ 1 whereas b = c (see [3] ).*Theorem*7.4. Assume h < b. ...##
###
Matrix iterations with vertical support restrictions
[article]

2018
*
arXiv
*
pre-print

of certain type of unbounded families on definable structures and of certain mad families (like those added by

arXiv:1803.05102v2
fatcat:ufk2lod4a5hq3dzuxx6dx733ce
*Hechler's*poset*for*adding an a.d. family) regardless of*the*cofinality of their size. ... As applications of this method, we show that a large class of FS iterations can preserve*the*mad family added by*Hechler's*poset (regardless of*the*cofinality of its size), and*the*consistency of a constellation ... IN201711, Dirección Operativa de Investigación, Institución Universitaria Pascual Bravo, and by*the*Grant-in-Aid*for*Early Career Scientists 18K13448, Japan Society*for**the*Promotion of Science. ...##
###
Template iterations and maximal cofinitary groups

2015
*
Fundamenta Mathematicae
*

In [2] , Jörg Brendle used

doi:10.4064/fm230-3-1
fatcat:znnpgvg3fjd4zawms6cu2d5zxe
*Hechler's*forcing notion*for*adding a maximal almost family along an appropriate template forcing construction to show that a (*the*minimal size of a maximal almost disjoint family ...*The*main result of*the*present paper is that ag,*the*minimal size of maximal cofinitary group, can be of countable cofinality. ... Using a combinatorial characterization of add(N ) and cof(N ) (*the*additivity and cofinality of*the**null**ideal*) due to Bartoszyński, we obtain that in*the*final generic extension both of those cardinal ...##
###
Template iterations and maximal cofinitary groups
[article]

2013
*
arXiv
*
pre-print

*The*main result of

*the*present paper is that a_g,

*the*minimal size of maximal cofinitary group, can be of countable cofinality. ... To prove this we define a natural poset

*for*adding a maximal cofinitary group of a given cardinality, which enjoys certain combinatorial properties allowing it to be used within a similar template forcing ... Using a combinatorial characterization of add(N ) and cof(N ) (

*the*additivity and cofinality of

*the*

*null*

*ideal*) due to Bartoszyński, we obtain that in

*the*final generic extension both of those cardinal ...

##
###
Some cardinal invariants of the generalized Baire spaces

2017
unpublished

We point out

doi:10.25365/thesis.47024
fatcat:carzzxpf3fav3mspiljb5cwxju
*the*similarities and differences with*the*classical case and explain*the*limitations of*the*classical methods when aiming*for*such generalizations. ...*The*central theme of*the*research in this dissertation is*the*well-known Cardinal invariants of*the*continuum. ... Then N is*the**ideal*of*null*subsets of 2 ω or ω ω with respect to*the*corresponding measure. ...