Absolutely integral homomorphisms

Absolutely Rigid Systems and Absolutely Indecomposable Groups

We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposable in any generic extension. However, any absolutely rigid family of groups has cardinality less than the partition cardinal κ(ω). Added December 2004: The proofs of Theorems 0.2 and 0.3 are not correct, and the clai...

Lattice Homomorphisms Induced by Group Homomorphisms

Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS

In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right con...

On Absolutely Continuous Transformations

POMDP Homomorphisms

The problem of finding hidden state in a POMDP and the problem of finding abstractions for MDPs are closely related. In this paper, we analyze the connection between existing Predictive State Representation methods [3] and homomorphic reductions of Markov Processes [5, 6]. We formally define a POMDP homomorphism, then extend PSR reduction methods to find POMDP homomorphisms when the original PO...