scholarly journals The left side of Cichoń’s diagram

2016 ◽  
Vol 144 (9) ◽  
pp. 4025-4042 ◽  
Author(s):  
Martin Goldstern ◽  
Diego Alejandro Mejía ◽  
Saharon Shelah
Keyword(s):  
Cichoń’S Diagram

scholarly journals COMPACT CARDINALS AND EIGHT VALUES IN CICHOŃ’S DIAGRAM

2018 ◽  
Vol 83 (2) ◽  
pp. 790-803 ◽  
Author(s):  
JAKOB KELLNER ◽  
ANDA RAMONA TĂNASIE ◽  
FABIO ELIO TONTI
Keyword(s):  
Cichoń’S Diagram ◽  
Image Position ◽  
Strongly Compact Cardinals

AbstractAssuming three strongly compact cardinals, it is consistent that$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) &#x003C; \mathfrakb &#x003C; \mathfrakd < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$Under the same assumption, it is consistent that$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) < non\left( {\cal M} \right) < cov\left( {\cal M} \right) < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$

Diamond principles in Cichoń’s diagram

2004 ◽  
Vol 44 (4) ◽  
pp. 513-526
Author(s):  
Hiroaki Minami
Keyword(s):  
Cichoń’S Diagram

More on Cichoń's diagram and infinite games

2000 ◽  
Vol 65 (4) ◽  
pp. 1713-1724 ◽  
Author(s):  
Masaru Kada
Keyword(s):  
Boolean Algebras ◽  
Infinite Games ◽  
Cardinal Invariants ◽  
Cichoń’S Diagram

AbstractSome cardinal invariants from Cichoń's diagram can be characterized using the notion of cut-and-choose games on cardinals. In this paper we give another way to characterize those cardinals in terms of infinite games. We also show that some properties for forcing, such as the Sacks Property, the Laver Property and ωω-boundingness, are characterized by cut-and-choose games on complete Boolean algebras.

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 COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS

2018 ◽  
Vol 83 (1) ◽  
pp. 208-236 ◽  
Author(s):  
VERA FISCHER ◽  
SY D. FRIEDMAN ◽  
DIEGO A. MEJÍA ◽  
DIANA C. MONTOYA
Keyword(s):  
Three Dimensional ◽  
Finite Support ◽  
Coherent Systems ◽  
Cichoń’S Diagram ◽  
Image Position ◽  
Generic Extensions

AbstractWe introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. 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. Furthermore, we show that this constellation of 7 values is consistent with the existence of a ${\rm{\Delta }}_3^1$ well-order of the reals.

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 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 Matrix iterations and Cichon’s diagram

2012 ◽  
Vol 52 (3-4) ◽  
pp. 261-278 ◽  
Author(s):  
Diego Alejandro Mejía
Keyword(s):  
Cichoń’S Diagram

Changing cardinal invariants of the reals without changing cardinals or the reals

1998 ◽  
Vol 63 (2) ◽  
pp. 593-599 ◽  
Author(s):  
Heike Mildenberger
Keyword(s):  
Measurable Cardinal ◽  
Consistency Strength ◽  
Cardinal Invariants ◽  
Inner Model ◽  
Cichoń’S Diagram

AbstractWe show: The procedure mentioned in the title is often impossible. It requires at least an inner model with a measurable cardinal. The consistency strength of changing and from a regular κ to some regular δ < κ is a measurable of Mitchell order δ. There is an application to Cichoń's diagram.

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