Related papers: On Tarski's fixed point theorem
On an infinite set some closure operators are finitary (algebraic) while others are not. We can generalize this idea for a complete algebraic lattice letting the compact elements act as the finite sets. With this in mind, we will consider…
Further extensions are given to the fixed point result (for implicit contractions) due to Altun and Simsek [Fixed Point Th. Appl., Volume 2010, Article ID 621469]. Some connections with related statements in the area due to Agarwal,…
We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many…
It is shown that the set of all finitary consequence operators defined on any nonempty language is a join-complete lattice. This result is applied to various collections of physical theories to obtain an unrestricted supremum unification.
We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…
We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained…
We discuss the possibility of representing supersymmetry exactly in a lattice discretized system. In particular, we construct a perfect supersymmetric action for the Wess-Zumino model.
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
Systems of fixpoint equations over complete lattices, consisting of (mixed) least and greatest fixpoint equations, allow one to express a number of verification tasks such as model-checking of various kinds of specification logics or the…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
A "Bochner-type" integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties…
I will give a presentation of an abstract approach to finite Ramsey theory found in an earlier paper of mine. I will prove from it a common generalization of Deuber's Ramsey theorem for regular trees and a recent Ramsey theorem of Jasinski…
Inspired by the work of Suzuki in [Proc. Amer. Math. Soc. 136 (2008), 1861--1869] we prove a fixed point theorem for contractive mappings that generalizes a theorem of Geraghty in [Proc. Amer. Math. Soc., 40 (1973), 604--608] and…
We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…
This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…
We introduce a new formulation of the axiom of dependent choice that can be viewed as an abstract termination principle, which generalises the recursive path orderings used to establish termination of rewrite systems. We consider several…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
Kotlarski's theorem (see H. Kotlarski. Bounded Induction and Satisfaction Classes. Mathematical Logic Quarterly, vol. 32, 31-34, 1986, P. 531--544.) formalized in $WKL_0$.
We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor iff A is an antilattice. We also generalize several other results of R. Kadison pertaining to infima and suprema in…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…