scholarly journals CLASS FORCING, THE FORCING THEOREM AND BOOLEAN COMPLETIONS

2016 ◽  
Vol 81 (4) ◽  
pp. 1500-1530 ◽  
Author(s):  
PETER HOLY ◽  
REGULA KRAPF ◽  
PHILIPP LÜCKE ◽  
ANA NJEGOMIR ◽  
PHILIPP SCHLICHT
Keyword(s):  
Combinatorial Property ◽  
Fundamental Result ◽  
Generic Extension ◽  
Negative Results ◽  
Generic Filter ◽  
Class Forcing

AbstractThe forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a condition in the relevant generic filter. We show that both the definability (and, in fact, even the amenability) of the forcing relation and the truth lemma can fail for class forcing.In addition to these negative results, we show that the forcing theorem is equivalent to the existence of a (certain kind of) Boolean completion, and we introduce a weak combinatorial property (approachability by projections) that implies the forcing theorem to hold. Finally, we show that unlike for set forcing, Boolean completions need not be unique for class forcing.

scholarly journals Outer models and genericity

2003 ◽  
Vol 68 (2) ◽  
pp. 389-418 ◽  
Author(s):  
M. C. Stanley
Keyword(s):  
Set Theory ◽  
Generic Extension ◽  
Transitive Model ◽  
Class Forcing ◽  
The Universe ◽  
Models Of Set Theory

Why is forcing the only known method for constructing outer models of set theory?If V is a standard transitive model of ZFC, then a standard transitive model W of ZFC is an outer model of V if V ⊆ W and V ∩ OR = W ∩ OR.Is every outer model of a given model a generic extension? At one point Solovay conjectured that if 0# exists, then every real that does not construct 0# lies in L[G], for some G that is generic for some forcing ℙ ∈ L. Famously, this was refuted by Jensen's coding theorem. He produced a real that is generic for an L-definable class forcing property, but does not lie in any set forcing extension of L.Beller, Jensen, and Welch in Coding the universe [BJW] revived Solovay's conjecture by asking the following question: Let a ⊆ ω be such that L[a] ⊨ “0# does not exist”. Is there ab∈ L[a] such that a ∉ L[b] and a is set generic over L[b].

Generic saturation

1998 ◽  
Vol 63 (1) ◽  
pp. 158-162
Author(s):  
Sy D. Friedman
Keyword(s):  
Generic Extension ◽  
Ground Model ◽  
Countable Ordinal ◽  
Homogeneous Set ◽  
Final Segment ◽  
Class Forcing

Assuming that ORD is ω + ω-Erdös we show that if a class forcing amenable to L (an L-forcing) has a generic then it has one definable in a set-generic extension of L[O#]. In fact we may choose such a generic to be periodic in the sense that it preserve the indiscernibility of a final segment of a periodic subclass of the Silver indiscernibles, and therefore to be almost codable in the sense that it is definable from a real which is generic for an L-forcing (and which belongs to a set-generic extension of L[0#]). This result is best possible in the sense that for any countable ordinal α there is an L-forcing which has generics but none periodic of period ≤ α. However, we do not know if an assumption beyond ZFC+“O# exists” is actually necessary for these results.Let P denote a class forcing definable over an amenable ground model 〈L, A〉 and assume that O# exists.Definition. P is relevant if P has a generic definable in L[0#]. P is almost relevant if P has a generic definable in a set-generic extension of L[0#].Remark. The reverse Easton product of Cohen forcings 2<κ, κ regular is relevant. So are the Easton product and the full product, provided κ is restricted to the successor cardinals. See Chapter 3, Section Two of Friedman [3]. Of course any set-forcing (in L) is almost relevant.Definition. κ is α-Erdös if whenever C is CUB in κ and f: [C]<ω → κ is regressive (i.e., f(a) < min(a)) then f has a homogeneous set of ordertype α.

Impairment Questions and Answers

1999 ◽  
Vol 4 (4) ◽  
pp. 4-4
Keyword(s):  
Symptom Validity ◽  
Validity Testing ◽  
Symptom Validity Testing ◽  
Negative Results ◽  
Tunnel Vision ◽  
Questions And Answers ◽  
Blurry Vision ◽  
Fatigue Evaluation ◽  
Choice Testing ◽  
Rule Out

Abstract Symptom validity testing, also known as forced-choice testing, is a way to assess the validity of sensory and memory deficits, including tactile anesthesias, paresthesias, blindness, color blindness, tunnel vision, blurry vision, and deafness—the common feature of which is a claimed inability to perceive or remember a sensory signal. Symptom validity testing comprises two elements: A specific ability is assessed by presenting a large number of items in a multiple-choice format, and then the examinee's performance is compared with the statistical likelihood of success based on chance alone. Scoring below a norm can be explained in many different ways (eg, fatigue, evaluation anxiety, limited intelligence, and so on), but scoring below the probabilities of chance alone most likely indicates deliberate deception. The positive predictive value of the symptom validity technique likely is quite high because there is no alternative explanation to deliberate distortion when performance is below the probability of chance. The sensitivity of this technique is not likely to be good because, as with a thermometer, positive findings indicate that a problem is present, but negative results do not rule out a problem. Although a compelling conclusion is that the examinee who scores below probabilities is deliberately motivated to perform poorly, malingering must be concluded from the total clinical context.

Needed: A publication of negative results: Comment.

1959 ◽  
Vol 14 (9) ◽  
pp. 598-598 ◽  
Author(s):  
Leroy Wolins
Keyword(s):  
Negative Results

Untersuchungen zur Quantifizierung der Änderung der Skelettmuskeldurchblutung nach Gefäßrevaskularisationen mit einem 99mTechnetiummarkierten Tracer

1990 ◽  
Vol 29 (05) ◽  
pp. 215-220 ◽  
Author(s):  
R. Benning ◽  
K. Nagel ◽  
M. Jugenheimer ◽  
S. Fischer ◽  
S. Worthmann ◽  
...  
Keyword(s):  
Transluminal Angioplasty ◽  
Lower Limbs ◽  
Surgical Patients ◽  
Treadmill Test ◽  
Negative Results ◽  
Clinical Observations ◽  
Before And After ◽  
Comparative Results ◽  
First Time ◽  
Percutaneous Transluminal

A new 99mTc-labelled tracer (99mTc-Sestanriibi) was used for the first time to demonstrate the perfusion of the skeletal muscle. In 16 patients with obstructive atherosclerosis of the lower limbs the change of perfusion of thigh and lower leg was studied with SPECT before and after vascular surgery (n = 11) or percutaneous transluminal angioplasty (n = 5). Comparative results of scintigraphic measurements and clinical observations (ancle-arm pressure, treadmill test) in 10 surgical patients (14 operated legs) showed correct positive or negative results in 86% (12/14).

Critical Evaluation of Impedance Phlebography for the Diagnosis of Deep Vein Thrombosis

1974 ◽  
Vol 31 (02) ◽  
pp. 273-278
Author(s):  
Kenneth K Wu ◽  
John C Hoak ◽  
Robert W Barnes ◽  
Stuart L Frankel
Keyword(s):  
Deep Vein Thrombosis ◽  
False Positive ◽  
False Negative ◽  
Critical Evaluation ◽  
Original Method ◽  
Vein Thrombosis ◽  
Negative Results ◽  
False Negative Results ◽  
Deep Vein ◽  
Positive Results

SummaryIn order to evaluate its daily variability and reliability, impedance phlebography was performed daily or on alternate days on 61 patients with deep vein thrombosis, of whom 47 also had 125I-fibrinogen uptake tests and 22 had radiographic venography. The results showed that impedance phlebography was highly variable and poorly reliable. False positive results were noted in 8 limbs (18%) and false negative results in 3 limbs (7%). Despite its being simple, rapid and noninvasive, its clinical usefulness is doubtful when performed according to the original method.

DETECTION OF XENOBIOTIC SUBSTANCES IN MUTE SWANS’ (CYGNUS OLOR) BLOOD

2015 ◽  
Author(s):  
Jolanta STANKEVIČIŪTĖ ◽  
Solveiga Marija BARKAUSKAITĖ ◽  
Gediminas BRAZAITIS
Keyword(s):  
Animal Species ◽  
Wild Animal ◽  
Wild Populations ◽  
New Methods ◽  
Negative Results ◽  
Cygnus Olor ◽  
Ecological Scale ◽  
Literature Reviews ◽  
Baseline Information ◽  
Mute Swans

During recent years the attention towards the effects of xenobiotic substances on wild nature has been steadily increasing. Literature reviews have revealed that active hormone-disintegrating substances might affect the reproduction of some wild animal species. Research shows anomalies of reproduction and development in various animal groups such as birds, fish, invertebrates and reptiles. Species inhabiting water and its surroundings cause the highest concern. Due to insufficient baseline information it is difficult to determine the extent of the problem in these wild populations on an ecological scale. The research described in this article is the first attempt to analyse xenobiotic substances and evaluate possible accumulation of pharmaceuticals in animals higher up in the food chain in Lithuania. This research tests new methods for to analyse for xenobiotics substances, which might be used in the future. Blood samples of 7 swans were examined using liquid chromatography, however, no xenobiotics were detected. Negative results do not eliminate the necessity for further investigate of larger samples, other species or to search for non-pharmaceutical xenobiotics.

The Nielsen-Thurston Classification

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Hyperbolic Geometry ◽  
Mapping Class Groups ◽  
Classification Theorem ◽  
Mapping Class ◽  
Fundamental Result ◽  
Class Groups ◽  
Mapping Torus ◽  
Higher Genus ◽  
Manifold Theory

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.

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