scholarly journals Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture

2005 ◽  
Vol 11 (2) ◽  
Author(s):  
P. Koszmider
Keyword(s):  
Banach Spaces ◽  
Chang’S Conjecture ◽  
Chang's Conjecture ◽  
Compactly Generated

scholarly journals Schauder decompositions in non-separable Banach spaces

1972 ◽  
Vol 6 (1) ◽  
pp. 133-144 ◽  
Author(s):  
J.J.M. Chadwick ◽  
R.W. Cross
Keyword(s):  
Banach Spaces ◽  
Separable Spaces ◽  
Compactly Generated

It is shown that Schauder decompositions exist in non-separable weakly compactly generated spaces and in certain non-separable conjugate spaces. Some results are obtained concerning shrinking and boundedly complete Schauder decompositions in non-separable spaces.

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 Twisted properties of banach spaces

2001 ◽  
Vol 89 (2) ◽  
pp. 217 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Manuel Gonzáles ◽  
Anatolij M. Plichko ◽  
David Yost
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Topological Properties ◽  
Space Property ◽  
Compactly Generated

If $\mathcal P$, $\mathcal Q$ are two linear topological properties, say that a Banach space $X$ has the property $\mathcal P$-by-$\mathcal Q$ (or is a $\mathcal P$-by-$\mathcal Q$ space) if $X$ has a subspace $Y$ with property $\mathcal P$ such that the corresponding quotient $X/Y$ has property $\mathcal Q$. The choices $\mathcal P,\mathcal Q \in\{\hbox{separable, reflexive}\}$ lead naturally to some new results and new proofs of old results concerning weakly compactly generated Banach spaces. For example, every extension of a subspace of $L_1(0,1)$ by a WCG space is WCG. They also give a simple new example of a Banach space property which is not a 3-space property but whose dual is a 3-space property.

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.

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