A Generalization of Moufang and Steiner Loops

We study a variety of loops, RIF, which arise naturally from considering inner mapping groups, and a somewhat larger variety, ARIF. All Steiner and Moufang loops are RIF, and all flexible C-loops are ARIF. We show that all ARIF loops are diassociative, thus generalizing Moufang's Theorem.Comment: 19 pp., 1 fig., uses amsart.cls, pifont.sty; to appear in Algebra Universali

Set mapping reflection

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that L(P(omega_1)) satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that combinatorial principle Square(kappa) fails for all regular kappa > omega_1.Comment: 11 page

Topological partition relations to the form omega^*-> (Y)^1_2

Theorem: The topological partition relation omega^{*}-> (Y)^{1}_{2} (a) fails for every space Y with |Y| >= 2^c ; (b) holds for Y discrete if and only if |Y| <= c; (c) holds for certain non-discrete P-spaces Y ; (d) fails for Y= omega cup {p} with p in omega^{*} ; (e) fails for Y infinite and countably compact

Efficient negation using abstract interpretation

While negation has been a very active área of research in logic programming, comparatively few papers have been devoted to implementation issues. Furthermore, the negation-related capabilities of current Prolog systems are limited. We recently presented a novel method for incorporating negation in a Prolog compiler which takes a number of existing methods (some modified and improved by us) and uses them in a combined fashion. The method makes use of information provided by a global analysis of the source code. Our previous work focused on the systematic description of the techniques and the reasoning about correctness and completeness of the method, but provided no experimental evidence to evalúate the proposal. In this paper, we report on an implementation, using the Ciao Prolog system preprocessor, and provide experimental data which indicates that the method is not only feasible but also quite promising from the efficiency point of view. In addition, the tests have provided new insight as to how to improve the proposal further. Abstract interpretation techniques are shown to offer important improvements in this application

A simultaneous generalization of independence and disjointness in boolean algebras

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.Comment: Sumbitted to Orde

A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page