We consider a class of Lindström extensions of first-order logic which are susceptible to a natural Skolemization procedure. In these logics Ehrenfeucht Mostowski (EM) functors for theories with arbitrarily large models can be obtained under suitable restrictions. Characteristic dependencies between algebraic properties of the quantifiers and the maximal domains of EM functors are investigated.Results are applied to Magidor Malitz logic,L(Q <ω), showing e.g. its Hanf number to be equal to ℶω(ℵ1) in the countably compact case. Using results of Baumgartner, the (...) maximal number of isomorphism types of linearly ordered models of regular cardinality is shown to be achieved for theories that admit an EM functor on a typically restricted domain. (shrink)

Heidorf, L., Moderate families in Boolean algebras, Annals of Pure and Applied Logic 57 217–250. A subset F of a Boolean algebra B will be called moderate if no element of B splits infinitely many elements of F . Disjoint moderate sets occur in connection with a product construction that is systematically studied in this paper. In contrast to the usual full direct product, these so-called moderate products preserve many properties of their factors. This can be used, for example, to (...) construct big retractive Boolean algebras that are not embeddable into interval algebras. The paper is also concerned with those Boolean algebras whose ideals are generated by moderate sets. The results may be summarized by saying that in many respects these algebras behave like countable ones. (shrink)

A partial ordering P is said to have the weak Freese-Nation property if there is a mapping tf : P → [P]0 such that, for any a, b ε P, if a b then there exists c ε tf∩tf such that a c b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g. under CH, (...) every ccc complete Boolean algebra has this property while, under b 2, there exists no complete Boolean algebra with the WFN. (shrink)