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

scholarly journals Some principles related to Chang's conjecture

1989 ◽  
Vol 45 (1) ◽  
pp. 39-101 ◽  
Author(s):  
Hans-Dieter Donder ◽  
Jean-Pierre Levinski
Keyword(s):  
Chang’S Conjecture ◽  
Chang's Conjecture
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