We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol...
It is consistent that there is a set mapping from the four-tuples of n into the finite subsets with no free subsets of size tn for some natural number tn. For any n < it is con...
Let X be a compact metric space. A closed set K X is located if the distance function d(x, K) exists as a continuous realvalued function on X; weakly located if the predicate d(x,...
The class of weakly algebrizable logics is defined as the class of logics having monotonic and injective Leibniz operator. We show that "monotonicity" cannot be discarde...
The choice construct (choose x : '(x)) is useful in software speci cations. We study extensions of rst-order logic with the choice construct. We prove some results about Hilb...