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Some principles related to Chang's conjecture

Hans-Dieter Donder, Jean-Pierre Levinski
1989 Annals of Pure and Applied Logic  
Concerning the third, shall Some principles reilated to Char@ conjecture 41  ...  This seems tc be a basic principle because it impiies the negation of Chang's conjecture, that no wl-complete uniform filter on o1 is wrsaturated and that every uniform ultrafilter on o1 is regular.  ...  Some principles reluted to Chung's conjecture ft to the reader. 0 85. The property <wl-Erdlis. Let P be the Levy-Solovay Wlb and follow the pattern of the proof of Theorem 8.8.  ... 
doi:10.1016/0168-0072(89)90030-4 fatcat:fbg64255vbaqnea6uwccbq7gqq

Chang's Conjecture with _ω_1, 2 from an ω_1-Erdős Cardinal [article]

Itay Neeman, John Susice
2019 arXiv   pre-print
Answering a question of Sakai, we show that the existence of an ω_1-Erdős cardinal suffices to obtain the consistency of Chang's Conjecture with _ω_1, 2. By a result of Donder this is best possible.  ...  We also give an answer to another question of Sakai relating to the incompatibility of _λ, 2 and (λ^+, λ) (κ^+, κ) for uncountable κ.  ...  Chang's Conjecture is known to be incompatible with Jensen's square principle ω1 (see [9] ) but was recently shown to be consistent with Schimmerling's square principle ω1,2 by Sakai [7] , assuming the  ... 
arXiv:1810.03511v4 fatcat:ef3thaeklvhmfbnc3ecyi7k4xq

Page 3797 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
Then Chang’s conjecture holds in any Pax extension of L(R).  ...  The author’s broadly applicable technique for incorporating Chang’s conjecture is to “stretch” countable substructures us- ing local elementary embeddings.  ... 

Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topics [article]

Sean Cox
2020 arXiv   pre-print
We survey some old and new results on strong variants of Chang's Conjecture and related topics.  ...  Those questions are related to Conjecture 4.8 below.  ...  Section 4, the longest section of the survey, deals with strong versions of Chang's Conjecture, stationary reflection principles, and related topics.  ... 
arXiv:1908.05334v3 fatcat:biqdu7miwrhkbjt7kjjbqzhygm

Chang's Conjecture and semiproperness of nonreasonable posets [article]

Sean D. Cox
2018 arXiv   pre-print
in the sense of Foreman-Magidor MR1359154---implies the version of Strong Chang's Conjecture from MR2723878 and MR1261218.  ...  One corollary of our work is that the version of Strong Chang's Conjecture from MR2965421 does not imply the existence of a precipitous ideal on ω_1.  ...  Some remarks about Strong Chang's Conjecture, special Aronszajn trees on ω 2 , and bounded dagger principles We call attention to the following two theorems: Theorem 25 (Todorcevic-Torres Perez [19], Theorem  ... 
arXiv:1605.00296v2 fatcat:chfnjm7gybdt7gbdere3qnc3ji

Page 5759 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
cannot be replaced by X; by the Chang’s conjecture result.  ...  Beyond that, it is an independently im- portant result that provides an optimal self-refinement of Chang’s conjecture in the partition calculus.  ... 

A variant of Shelah's characterization of Strong Chang's Conjecture [article]

Sean Cox, Hiroshi Sakai
2018 arXiv   pre-print
Shelah considered a certain version of Strong Chang's Conjecture, which we denote SCC^cof, and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper  ...  This strengthens and sharpens the results of Cox, and sheds some light on problems from Usuba and Torres-Perez and Wu.  ...  another version of Strong Chang's Conjecture, denoted SCC split , and prove Theorem 1.2 below, which is analogous to Shelah's Theorem 1.  ... 
arXiv:1811.06402v1 fatcat:6xdv5gfrcbcmdpj6esr623vtba

Strong Chang's Conjecture and the tree property at ω2

Víctor Torres-Pérez, Liuzhen Wu
2015 Topology and its Applications  
We prove that a strong version of Chang's Conjecture, equivalent to the Weak Reflection Principle at ω_2, together with 2^ω=ω_2, imply there are no ω_2-Aronszajn trees.  ...  Some final remarks We mention some related previous results. R. Strullu proved that the Map Reflection Principle, introduced by Moore in [7] , together with MA ω 1 implies TP(ω 2 ) (see [12] ).  ...  Consider the following strong version of Chang's Conjecture: Definition 3.1 (CC * ).  ... 
doi:10.1016/j.topol.2015.05.061 pmid:26973369 pmcid:PMC4784726 fatcat:ypffeueyvjgcplp4ycegxl66p4

Page 636 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
Lévy (IL-HEBR) 91b:03087 03E35 03505 Donder, Hans-Dieter (D-FUB-2); Levinski, Jean-Pierre (1-DTM) Some principles related to Chang’s conjecture. Ann. Pure Appl. Logic 45 (1989), no. 1, 39-101.  ...  ~TH was already known to lie between the full Chang conjecture (CC) and the weak variant of Chang’s conjecture (wCC) introduced by Shelah when considering cardinal exponentiation.  ... 

Global Chang's Conjecture and singular cardinals [article]

Monroe Eskew, Yair Hayut
2021 arXiv   pre-print
We show some ZFC limitations on such principles, and prove relative to large cardinals that Chang's Conjecture can consistently hold between all pairs of limit cardinals below ℵ_ω^ω.  ...  We investigate the possibilities of global versions of Chang's Conjecture that involve singular cardinals.  ...  "Chang's Conjecture" is a type of principle strengthening this theorem to assert similar relationships between sequences of cardinals.  ... 
arXiv:1812.11768v2 fatcat:rkoksafk7fcexnf56e5tcngamu

Global Chang's Conjecture and singular cardinals

Monroe Eskew, Yair Hayut
2021 European Journal of Mathematics  
We show some $$\mathrm{ZFC} $$ ZFC limitations on such principles and prove relative to large cardinals that Chang's Conjecture can consistently hold between all pairs of limit cardinals below $$\aleph  ...  AbstractWe investigate the possibilities of global versions of Chang's Conjecture that involve singular cardinals.  ...  "Chang's Conjecture" is a type of principle strengthening this theorem to assert similar relationships between sequences of cardinals.  ... 
doi:10.1007/s40879-021-00459-8 pmid:34722125 pmcid:PMC8550154 fatcat:4i2wt5y33nbv7bpdkyb2rwltla

Club Chang's Conjecture [article]

Sean Cox, Saharon Shelah
2019 arXiv   pre-print
Chang's Conjecture (CC) asserts that for every F:[ω_2]^<ω→ω_2, there exists an X that is closed under F such that |X|=ω_1 and |X ∩ω_1| =ω.  ...  We denote this stronger principle Club-CC, and also show that, unlike CC, Club-CC implies failure of certain weak square principles.  ...  Then Club Chang's Conjecture holds in V 3 by Theorem 15.  ... 
arXiv:1809.09280v4 fatcat:tmkvhdxpcrhw5nzukqr25lg2yy

On the divisible parts of quotient groups [article]

Andreas Blass
1993 arXiv   pre-print
Techniques of combinatorial set theory are applied to the following algebraic problem.  ...  We shall need an elementary connection between Chang's conjecture and the compression principle and a (nonelementary) theorem from [7] giving the consistency of a particular instance of Chang's conjecture  ...  The counterexample involves Chang's conjecture.  ... 
arXiv:math/9310210v1 fatcat:dscbtn7dsnfxbbajqi7xfwso3a

Magidor-Malitz Reflection [article]

Yair Hayut
2018 arXiv   pre-print
We derive some combinatorial results and improve the known upper bound for the consistency of Chang's Conjecture at successor of singular cardinals.  ...  In section 2 we define the Q <ω analogue for Chang's conjecture and derive some reflection principles from it.  ...  CONSISTENCY RESULTS This section is dedicated to the derivation of some consistency results regarding the reflection principles that were defined above. 3.1. Chang's conjecture at ℵ ω+1 .  ... 
arXiv:1512.09299v4 fatcat:h2iqg67efje5jbolmmgaendvju

Stationary and Closed Rainbow subsets [article]

Shimon Garti, Jing Zhang
2020 arXiv   pre-print
In the process of dealing with cardinals greater than ω_1, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question  ...  When compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as  ...  Versions of Chang's Conjectures and rainbow sets The following boundedness condition naturally arises when versions of Chang's Conjectures are applied to study rainbow Ramsey theory. Definition 2.1.  ... 
arXiv:2007.05935v1 fatcat:njmkayay7bhkpenpq4p6tus2vq
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