HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS

2018 ◽  
Vol 83 (1) ◽  
pp. 283-325 ◽  
Author(s):  
GUNTER FUCHS
Keyword(s):  
Forcing Axioms ◽  
Level I ◽  
Consistency Strengths ◽  
Extendible Cardinals

AbstractI analyze the hierarchies of the bounded resurrection axioms and their “virtual” versions, the virtual bounded resurrection axioms, for several classes of forcings (the emphasis being on the subcomplete forcings). I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for subcomplete or countably closed forcing imply the failure of Todorčević’s square at the appropriate level. I also establish connections between these hierarchies and the hierarchies of bounded and weak bounded forcing axioms.

ON RESURRECTION AXIOMS

2015 ◽  
Vol 80 (2) ◽  
pp. 587-608 ◽  
Author(s):  
KONSTANTINOS TSAPROUNIS
Keyword(s):  
Lower Bounds ◽  
Forcing Axioms ◽  
Extendible Cardinals ◽  
Weak Square

AbstractThe resurrection axioms are forms of forcing axioms that were introduced recently by Hamkins and Johnstone, who developed on earlier ideas of Chalons and Veličković. In this note, we introduce a stronger form of resurrection (which we callunboundedresurrection) and show that it gives rise to families of axioms which are consistent relative to extendible cardinals, and which imply the strongest known instances of forcing axioms, such as Martin’s Maximum++. In addition, we study the unbounded resurrection postulates in terms of consistency lower bounds, obtaining, for example, failures of the weak square principle.

Hierarchies of forcing axioms I

2008 ◽  
Vol 73 (1) ◽  
pp. 343-362 ◽  
Author(s):  
Itay Neeman ◽  
Ernest Schimmerling
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Large Cardinal ◽  
Forcing Axioms ◽  
Consistency Strengths

AbstractWe prove new upper bound theorems on the consistency strengths of SPFA(θ), SPFA(θ-linked) and SPFA(θ+ -cc). Our results are in terms of (θ, Γ)-subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γ-indescribability. Our upper bound for SPFA(ϲ-linked) has a corresponding lower bound, which is due to Neeman and appears in his follow-up to this paper. As a corollary, SPFA(ϲ-linked) and PFA(ϲ-linked) are each equiconsistent with the existence of a -indescribable cardinal. Our upper bound for SPFA(ϲ-c.c) is a -indescribable cardinal, which is consistent with V = L. Our upper bound for SPFA(ϲ+-linked) is a cardinals κ that is (κ+,)-subcompact, which is strictly weaker than κ+-supercompact. The axiom MM(ϲ) is a consequence of SPFA(ϲ+-linked) by a slight refinement of a theorem of Shelah. Our upper bound for SPFA(ϲ++-c.c.) is a cardinal κ that is (κ+, )-subcompact, which is also strictly weaker than κ+-supercompact.

HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES

2018 ◽  
Vol 83 (1) ◽  
pp. 256-282 ◽  
Author(s):  
GUNTER FUCHS
Keyword(s):  
Continuum Hypothesis ◽  
Reflection Principle ◽  
Forcing Axioms ◽  
Subcomplete Forcing ◽  
Square Principles ◽  
Consistency Strengths ◽  
Remarkable Cardinals ◽  
Forcing Axiom ◽  
The Continuum

AbstractI analyze the hierarchies of the bounded and the weak bounded forcing axioms, with a focus on their versions for the class of subcomplete forcings, in terms of implications and consistency strengths. For the weak hierarchy, I provide level-by-level equiconsistencies with an appropriate hierarchy of partially remarkable cardinals. I also show that the subcomplete forcing axiom implies Larson’s ordinal reflection principle atω2, and that its effect on the failure of weak squares is very similar to that of Martin’s Maximum.

Neue endoluminale und chirurgische Verfahren für die Behandlung der morbiden Adipositas

2019 ◽  
Vol 76 (3) ◽  
pp. 138-142 ◽  
Author(s):  
Tarik Delko
Keyword(s):  
Gastric Bypass ◽  
Chirurgische Verfahren ◽  
Level I

Zusammenfassung. Bei der Behandlung der (morbiden) Adipositas wurden neu auch endoluminale Verfahren entwickelt, mit dem Ziel, schonungsvollere und für den Patienten eher akzeptable Methoden anzubieten. Mehrere dieser mittels Gastroskopie im oberen Magendarmtrakt durchführbaren Eingriffe werden vorgestellt. In der Schweiz sollten durch interdisziplinäre Arbeitsgruppen Studien designt werden, die deren Wirksamkeit und Sicherheit langfristig aufzeigen. Zwischenzeitlich sind diese endoluminalen Methoden als hoch experimentelle Verfahren an zu sehen und so dem betroffenen Patienten zu kommunizieren. Zudem werden neuere chirurgische Verfahren vorgestellt. Insbesondere der One Anastomis Gastric Bypass (OAGB) wird aufgrund vermehrter Level I Evidenz weltweit zunehmend akzeptiert, viele Befürchtungen haben sich nach 21 Jahren nicht bestätigt. Weitere Ergebnisse aus randomisiert kontrollierten Studien werden in naher Zukunft folgen und könnten als Basis dienen, dieses Verfahren auch in der Schweiz als etablierte Technik freizugeben.

Wie viele Zertifizierungen brauchen wir noch? Wird die Qualität in Perinatalzentren Level I durch Zertifizierung besser?

2013 ◽  
Vol 217 (S 01) ◽  
Author(s):  
T Ernst ◽  
P Kiene ◽  
AK Kämpf ◽  
J Lange ◽  
S Grüßner ◽  
...  
Keyword(s):  
Level I
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