the aim of this paper is to study orders over a valuation ring v with arbitrary rank in acentral simple f-algebra q. the relation between all of the orders is explained with a diagram. it is thenshown that inside bezout order, extremal v-orders are precisely semi-hereditary. in the last section, theeffect of henselization on maximal and semi-hereditary orders is examined.

This is a survey of recent work on the structure of Tukey reductions among analytic σ-ideals of compact subsets of compact metric spaces and analytic P-ideals of sets of natural numbers. An attempt is made to organize the results into a unified whole. This organization makes it possible to identify natural unresolved problems. Some new joint results with Stevo Todorcevic are announced. This pap...

We experimentally analyze equilibrium discovery in i) a pure call auction, ii) a call auction preceded by a nonbinding preopening period, and iii) a call auction preceded by a binding preopening period. We examine whether a preopening period can facilitate coordination on the Pareto dominant equilibrium. During the nonbinding preopening period, traders tend to place manipulative orders. After o...

Trotter conjectured that dim P × Q ≥ dimP + dimQ − 2 for all posets P and Q. To shed light on this, we study the k-dimension of products of finite orders. For k ∈ o(ln lnn), the value 2 dimk(P )−dimk(P ×P ) is unbounded when P is an n-element antichain, and 2dim2(mP ) − dim2(mP × mP ) is unbounded when P is a fixed poset with unique maximum and minimum. For products of the “standard” orders Sm ...

We study two kinds of segment orders, using definitions first proposed by Farhad Shahrokhi. Although the two kinds of segment orders appear to be quite different, we prove several results suggesting that the are very much the same. For example, we show that the following classes belong to both kinds of segment orders: (1) all posets having dimension at most 3; (2) interval orders; and for n ≥ 3...

A finite poset is an angle order if its points can be mapped into angular regions in the plane so that x precedes y in the poset precisely when the region for x is properly included in the region for y. We show that all posets of dimension four or less are angle orders, all interval orders are angle orders, and that some angle orders must have an angular region less than 180” (or more than 180”...

This paper is devoted to the study of contiguity orders i.e. orders having a linear extension L such that all upper (or lower) cover sets are intervals of L. This new class is a strict generalization of both interval orders and N{free orders, and is linearly recognizable. It is proved that computing the number of contiguity extensions is #P{complete, and that the dimension of height one contigu...

let f, g and h be all entire functions of several complex variables. in this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

in this paper, it is proved that all simple $k_4$-groups of type $l_2(q)$ can be characterized by their maximum element orders together with their orders. furthermore, the automorphism groups of simple $k_4$-groups of type $l_2(q)$ are also considered.

In the paper I suggested that for many predicates P, the 'P-er than' relation is a strict weak order. Ondrej Majer asks why I assume that, given that I concentrate myself later in the paper on semi-orders. Well, in case the ordering relation can be made more precise by means of measurement phrases, there is no choice but to use a strict weak order. In fact, speaker's intuitions about a relation...