scholarly journals Cichoń’s diagram and localisation cardinals

2020 ◽  
Author(s):  
Martin Goldstern ◽  
Lukas Daniel Klausner
Keyword(s):  
Countable Support ◽  
Link Type ◽  
Cardinal Characteristics ◽  
Cichoń’S Diagram ◽  
Creature Forcing

Abstract We reimplement the creature forcing construction used by Fischer et al. (Arch Math Log 56(7–8):1045–1103, 2017. 10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.

scholarly journals Creature forcing and five cardinal characteristics in Cichoń’s diagram

2017 ◽  
Vol 56 (7-8) ◽  
pp. 1045-1103 ◽  
Author(s):  
Arthur Fischer ◽  
Martin Goldstern ◽  
Jakob Kellner ◽  
Saharon Shelah
Keyword(s):  
Cardinal Characteristics ◽  
Cichoń’S Diagram ◽  
Creature Forcing

scholarly journals Another ordering of the ten cardinal characteristics in Cichoń's diagram

2019 ◽  
Vol 60 (1) ◽  
pp. 61-95
Author(s):  
 Kellner Jakob ◽  
Shelah Saharon ◽  
Tănasie Anda R.
Keyword(s):  
Cardinal Characteristics ◽  
Cichoń’S Diagram

scholarly journals Decisive creatures and large continuum

2009 ◽  
Vol 74 (1) ◽  
pp. 73-104 ◽  
Author(s):  
Jakob Kellner ◽  
Saharon Shelah
Keyword(s):  
Countable Support ◽  
Large Continuum ◽  
Dual Notion ◽  
Creature Forcing ◽  
Countable Support Iteration

AbstractFor f, g ∈ ωω let be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch v of the f-tree, one of the g-trees contains v. is the dual notion: For every branch v, one of the g-trees guesses v(m) infinitely often.It is consistent that for ℵ1 many pairwise different cardinals κ∊ and suitable pairs (f∊, g∊).For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision.

scholarly journals Preservation of splitting families and cardinal characteristics of the continuum

2021 ◽  
Author(s):  
Martin Goldstern ◽  
Jakob Kellner ◽  
Diego A. Mejía ◽  
Saharon Shelah
Keyword(s):  
Finite Support ◽  
Cardinal Characteristics ◽  
Splitting Number ◽  
Cichoń’S Diagram ◽  
Dependent Entries ◽  
The Continuum

AbstractWe show how to construct, via forcing, splitting families that are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cichoń’s diagram, $$\mathfrak{m}$$ m (2-Knaster), $$\mathfrak{p}$$ p , $$\mathfrak{h}$$ h , the splitting number $$\mathfrak{s}$$ s and the reaping number $$\mathfrak{r}$$ r .

scholarly journals Controlling cardinal characteristics without adding reals

2020 ◽  
pp. 2150018
Author(s):  
Martin Goldstern ◽  
Jakob Kellner ◽  
Diego A. Mejía ◽  
Saharon Shelah
Keyword(s):  
Cardinal Characteristics ◽  
Cichoń’S Diagram ◽  
New Formula

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber.

SIG 15 Perspectives Vol. 20, No. 3, September 2015

2015 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Learning Center ◽  
Link Type

Abstract Download the CE Questions PDF from the toolbar, above. Use the questions to guide your Perspectives reading. When you're ready, purchase the activity from the ASHA Store and follow the instructions to take the exam in ASHA's Learning Center. Available until August 13, 2018.

SIG 11 Perspectives Vol. 22, No. 2, July 2012

2012 ◽  
Vol 22 (2) ◽  
Author(s):  
Kathryn Taylor ◽  
Emily White ◽  
Rachael Kaplan ◽  
Colleen M. O'Rourke
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 11 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 14 Perspectives Vol. 20, No. 3, December 2013

2013 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 14 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 17 Perspectives Vol. 2, No. 1, May 2012

2012 ◽  
Vol 2 (1) ◽  
pp. 1-5
Author(s):  
Celeste Domsch
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 17 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 12 Perspectives Vol. 21, No. 4, December 2012

2012 ◽  
Vol 21 (4) ◽  
pp. 1-6 ◽  
Author(s):  
Cathy Binger ◽  
Jennifer Kent-Walsh
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 12 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

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