In [4] we characterize the class of countable completey representable relation and cylindric algebras via special neat embeddings. In this note we provide a counterexample showing that the condition of countability cannot be omitted.

We present a summary of the lectures delivered to the Institute for Mathematical Sciences, Singapore, during the 2005 Summer School in Mathematical Logic. The lectures covered topics on the global structure of the Turing degrees D, the countability of its automorphism group, and the definability of the Turing jump within D.

There is an ongoing debate regarding the syntactic and semantic nature of the mass versus count-noun distinction. If we concentrate solely on the semantic side of the debate, we can distinguish two families of approaches. The first approach, represented, for instance, by Link (1983) and Chierchia (1998), among others, argues that the difference between mass and count can be reduced to homogenei...

In this paper we will prove the Urysohn Meterization Theorem, which gives sufficient conditions for a topological space to be metrizable. In the process of proving this theorem, we will the discuss separation and countability axiom of topological spaces and prove the Urysohn Lemma.

Let U ′′ = 2 be arbitrary. In [1], the main result was the derivation of multiply linear isomorphisms. We show that sM is countably negative definite and extrinsic. In [1], the authors described projective planes. It is well known that 0×N > { limB ( 1 0 , 0−2 ) , ε ≤ ∅ ∫ I′′ exp (G ′(χ) + 1) dm, ‖d(c)‖ ⊃ I .