Two important results in quadratic form theory, Pfister’s local-global principle and the isotropy theorem (see [5]), can be stated more generally for spaces of orderings (an abstract version of real spectras of formally real fields), for which they are expressed as local-global principles: A property of quadratic forms (expressed as a so-called positive-primitive formula) holds if and only if i...

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris’ Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well-quasi-ordering of finite sequences of natural nu...

A model of phase field has been developed to investigate the microstructure evolution during selective laser melting (SLM) of metal powder bed. A two-component (degree of order, orientation field) ordering parameter has been used, for which the permissive relationships have been derived reasoning from the principle of entropy production positivity. The application of this principle has made pos...

It is well known that appropriate variable and value ordering heuristics are often crucial when solving constraint satisfaction problems. A variable ordering heuristic which is often recommended, and is often successful, is based on the `failrst' principle: choose next the variable with the smallest remaining domain. General-purpose value ordering heuristics are less common, but it has been arg...

The international Classification of Primary Care (ICPC) has now been available to the family medicine community for a decade as the main ordering principle of its domain. Research data and practical experiences with ICPC, as well as the development of new concepts in family medicine, have resulted in new applications. The structure of episodes of care to be included in a computer-based patient ...

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys “continuity for easy cases,” i.e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also – rather counter-intuitively – allow chances of small improvements to compensate risks of huge lo...

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators de ned on them. That means in particular that the choice of the underlying partial ordering is of eminent importance, as it determines the class of morphological operators that one ends up with. The duality principle for partially ordered sets, which says that the opposite of a par...

We introduce two games played on positive braids. The first game is played on 3-strand positive braids and its termination time is Ackermannian in the input. We give an ordinal-theoretic and a model-theoretic proof (using semi-regular cuts in models of arithmetic). The second game is played on arbitrary positive braids and its termination is unprovable in IΣ2, the two-quantifier induction arith...