"In a progression of theories based on an initial theory of numbers, one attempts to overcome incompleteness by successively adding consistency statements or stronger principles reflecting on the systems in question," Feferman explained in an e-mail interview.
Using a formulation of this idea in terms of a transfinite progression of theories, Feferman determined the exact limit of predicativity as measured by a certain transfinite ordinal number.
The progression of quantum theory beyond physics, into chemistry, and possibly thence into biology, will probably astonish the people who are investigating it now, and who may have thought they knew what they were up to all along.
At the time, Pitt Rivers' ideas seemed to be a logical progression of evolutionary theory, which was believed to be applicable in many fields other than biology.
The progression of migration theory from the relatively simple, perfect-markets neoclassical model to NELM models involves both increasing complexity and more generality in how we think about migration determinants and impacts.
The association between poor prognosis and cytoplasmic EGFR staining may be due to changes in ligand EGFR complex internalisation and activation of associated signalling pathways in the progression of RCC, the theory that Piyathilake et al have further strengthened by cell culture experiments.
In a seminal paper, Lin and Reiter introduced a model-theoretic definition for the progression of a basic action theory in the situation calculus, and proved that it implies the intended properties.
In this review, we detail the theory and progression of AFM-based nanoindentation, and present several applications of this technique as it has been used to probe biomolecules and biological nanostructures from single proteins to complex assemblies.
Spatiotemporal crime analyses are appearing much more frequently in our academic literature in recent years and have become a principal contributor to the progression of routine activities, crime pattern theory, place-management and situational crime prevention.
Under the assumptions of the first theory, the progression of cancer through its first stages is sequential and forms a single lineage due to the low normal mutation rate which reduces the chances that a new positively selected phenotype arises more than once during early stages of clonal expansion.
