The aim of the paper is to develop the notion of partial probability distributions as being more realistic models of belief systems than the standard accounts. We formulate the theory of partial probability functions independently of any classical semantic notions. We use the partial probability distributions to develop a formal semantics for partial propositional calculi, with extensions to predicate logic and higher order languages. We give a proof theory for the partial logics and obtain soundness and completeness results.

Theorem: For every k, there is an expansion of the theory of algebraically closed fields (of any fixed characteristic) which is almost strongly minimal with Morley rank k.

The purpose of this paper is mainly to give a model of paraconsistent logic satisfying the "Frege comprehension scheme" in which we can develop standard set theory (and even much more as we shall see). This is the continuation of the work of Hinnion and Libert.

We survey various results on the relationship among neat embeddings (a notion special to cylindric algebras), complete representations, omitting types, and amalgamation. A hitherto unpublished application of algebraic logic to omitting types of first-order logic is given.

We show that the property of sequential compactness for subspaces of 𝕉 is countably productive in ZF. Also, in the language of weak choice principles, we give a list of characterizations of the topological statement 'sequentially compact subspaces of 𝕉 are compact'. Furthermore, we show that forms 152 (= every non-well-orderable set is the union of a pairwise disjoint well-orderable family of denumerable sets) and 214 (= for every family A of infinite sets there is a function f such that for all y∊ A, f(y) is a nonempty subset of y and ∣ f(y) ∣ = א₀) of Howard and Rubin are equivalent.

That the result of flipping quantifiers and negating what comes after, applied to branching-quantifier sentences, is not equivalent to the negation of the original has been known for as long as such sentences have been studied. It is here pointed out that this syntactic operation fails in the strongest possible sense to correspond to any operation on classes of models.