Families for which the consistency conditions are satisfied are called consistent families, and it is only for this restricted class that the laws of quantum dynamics for a closed system can be used to assign a meaningful set of probabilities.
What Gödel's result showed was that there can be no absolute consistency proof of all of mathematics; hence work in proof theory after Gödel concentrated on relative results, both: relative to the system for which a consistency proof was given, and relative to the proof methods used.
Next, 38 items were selected at random from the other 7 cells, yielding a nucleus of 304 words for which frequency, consistency, and imageability were uncorrelated.
The first difficulty Frege notes with Hilbert's approach is that it is not clear what Hilbert means by "axioms:" if he means the kinds of things for which issues of consistency and independence can arise, then he must be talking about thoughts, while if he means the kinds of things which are susceptible of multiple interpretations, then he must be talking about sentences.
The coefficients ranged from.75 to.91 in the Québec sample, and from.75 to.92 in the French sample, except for the Relaxation scale for which the internal consistency coefficient was.68 in the French sample.
In this paper we describe a simple algebraic property which characterises all possible constraint types for which strong k-consistency is sufficient to ensure global consistency, for each k > 2. We give a number of examples to illustrate the application of this result.
In particular, Feferman pointed to intensional problems connected to the notion of axiomhood by exhibiting a non-standard though extensionally (i.e., numerically) correct binumeration of the arithmetic theory T under consideration, for which the (intensionally incorrect) consistency statement can be proved by T.
Patient 9 formed an exception to this consistency, for which six CGCs reported a causal mutation in MYBPC3 (Table 2).
A quarter of the data were double-coded to check for consistency, for which there was >90% agreement between researchers (RP and AG).
For 11 out of 22 questionnaires for which information on internal consistency was found, factor analysis was applied before calculating Cronbach's α.
