scholarly journals A variant of Shelah's characterization of Strong Chang's Conjecture

2019 ◽  
Vol 65 (2) ◽  
pp. 251-257
Author(s):  
Sean Cox ◽  
Hiroshi Sakai
Keyword(s):  
Chang’S Conjecture ◽  
Chang's Conjecture

scholarly journals Normality Versus Paracompactness in Locally Compact Spaces

2018 ◽  
Vol 70 (1) ◽  
pp. 74-96 ◽  
Author(s):  
Alan Dow ◽  
Franklin D. Tall
Keyword(s):  
Strong Form ◽  
Locally Compact ◽  
Compact Spaces ◽  
Correct Proof ◽  
Chang’S Conjecture ◽  
Collectionwise Hausdorff ◽  
Chang's Conjecture ◽  
Paracompact Spaces ◽  
Locally Compact Spaces

AbstractThis note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on ω1, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of ω1.

scholarly journals Some two-cardinal results for O-minimal theories

1998 ◽  
Vol 63 (2) ◽  
pp. 543-548 ◽  
Author(s):  
Timothy Bays
Keyword(s):  
Minimal Theory ◽  
Chang’S Conjecture ◽  
Chang's Conjecture

AbstractWe examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ′, λ′). We also prove that every “reasonable” variant of Chang's Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the δ-cardinal case for arbitrary ordinals δ.

scholarly journals LOCAL CLUB CONDENSATION AND L-LIKENESS

2015 ◽  
Vol 80 (4) ◽  
pp. 1361-1378
Author(s):  
PETER HOLY ◽  
PHILIP WELCH ◽  
LIUZHEN WU
Keyword(s):  
Regular Cardinal ◽  
Large Cardinal ◽  
Ground Model ◽  
The Third ◽  
Chang’S Conjecture ◽  
Chang's Conjecture ◽  
Generalized Condensation

AbstractWe present a forcing to obtain a localized version of Local Club Condensation, a generalized Condensation principle introduced by Sy Friedman and the first author in [3] and [5]. This forcing will have properties nicer than the forcings to obtain this localized version that could be derived from the forcings presented in either [3] or [5]. We also strongly simplify the related proofs provided in [3] and [5]. Moreover our forcing will be capable of introducing this localized principle at κ while simultaneously performing collapses to make κ become the successor of any given smaller regular cardinal. This will be particularly useful when κ has large cardinal properties in the ground model. We will apply this to measure how much L-likeness is implied by Local Club Condensation and related principles. We show that Local Club Condensation at κ+ is consistent with ¬☐κ whenever κ is regular and uncountable, generalizing and improving a result of the third author in [14], and that if κ ≥ ω2 is regular, CC(κ+) - Chang’s Conjecture at κ+ - is consistent with Local Club Condensation at κ+, both under suitable large cardinal consistency assumptions.

On A Variant of Weak Chang's Conjecture

1991 ◽  
Vol 37 (19-22) ◽  
pp. 289-292
Author(s):  
Yasuo Kanai
Keyword(s):  
Chang’S Conjecture ◽  
Chang's Conjecture

Chang’s conjecture for ℵω

1990 ◽  
Vol 69 (2) ◽  
pp. 161-172 ◽  
Author(s):  
Jean-Pierre Levinski ◽  
Menachem Magidor ◽  
Saharon Shelah
Keyword(s):  
Chang’S Conjecture ◽  
Chang's Conjecture
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