Fixedpoint theorems play a fundamental role in denotational semantics of programming languages. In 1955, Tarski [6] and Davis [l] showed that a lattice L is complete if and only if every monotonic function f: L + L has a fixedpoint. Since then, other fixedpoint properties are considered, by imposing either the function to be o-continuous or the fixedpoint to be the least fixedpoint. The key que...

If X"0, Xx_ is an arbitrarily-dependent sequence of random variables taking values in [0,1] and if V( X0,X¡,... ) is the supremum, over stop rules /, of EX,, then the set of ordered pairs {(.*, v): x V(X0, Xx,.. .,Xn) and y £(maxyS„X¡) for some X0,..., Xn] is precisely the set C„= {(x,y):x<y<x(\ + n(\ *'/")); 0 « x « l}; and the set of ordered pairs {(x, y): x V(X0, X,,...) and y £(sup„ X„) for...

The COCOLOG system is a partially ordered family of rst order logical theories that describe the controlled evolution of the state of a given partially observered-nite machine M. Following the review of the general COCOLOG system and its Markovain fragment system , a mutil-complexity measurement called Joint is deened and further a partial order simplicity is introduced. Finally, some compariso...

We consider classes of relation algebras expanded with new operations based on the formation of ordered pairs. Examples for such algebras are pairing (or projection) algebras of algebraic logic and fork algebras of computer science. It is proved in Sain{N emeti 36] that there is nòstrong' representation theorem for all abstract pairing algebras in most set theories including ZFC as well as most...

This paper consists of two parts. In the first auxilliary part, we deal with sets with cyclic order. For any such set O we introduce following [BG] a cocycle l : G × G → Z valued in {0,±1} ⊂ Z on the group G of automorphisms of O. The cohomology class of l in H(G,Z) will be called the Euler class. If K is an ordered field, then the projective line P(K) has a cyclic order and PSL2(K) acts orderp...