1,721,078 research outputs found
Extending addition in Elliott's local semigroup
No full textWe study the unique extendability of Elliott′s partial addition of Murray-von Neumann equivalence classes of projections in AF C*-algebras. We prove that there is at most one commutative associative monotone extension satisfying the natural residuation condition that for each projection p the class of 1 - p is the smallest one whose sum with the class of p equals 1. We prove that for every AF C*-algebra A this associative commutative monotone residual extension exists if, and only if, the Murray-von Neumann order on equivalence classes of projections in A is a lattice order. By Elliott′s classification theorem, the resulting monoid uniquely characterizes A. We give a simple equational characterization of the monoids arising as classifiers
Decidable and undecidable prime theories in infinite-valued logic
No full textIn classical propositional logic, a theory T is prime (i.e., for every pair of formulas F,G, either T⊢F→G or T⊢G→F) iff it is complete. In Lukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free l-groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable (r.e.) prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory over countably many variables
A Cantor-Bernstein theorem for -complete MV-algebras
No full textsummary:The Cantor-Bernstein theorem was extended to -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras
A constructive proof that every 3-generated l-group is ultrasimplicial
No full textWe discuss the ultrasimplicial property of lattice-ordered abelian groups and their associated MV-algebras. We give a constructive proof of the fact that every lattice-ordered abelian group generated by three elements is ultrasimplicial
COSSAC: Combinatorics of Sorting, Searching, and Coding,
No full textSpecial Issue of the journal Discrete Applied Mathematic
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