A Completenes Theorem for an Infinitary Intutionistic Logic With Both Ordinary and Probability Quantifiers
Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier .
An existence theorem for 1-atomic standard models of (more weak than usual “atomic models”) and applications of to are the results of this note.
Let be the set of subsets of of cardinality . Let be a coloring of and a coloring of . We write if every -homogeneous is also -homogeneous. The least such that for some is called the -width of and denoted by . In the first part of the paper we prove the existence of colorings with high -width. In particular, we show that for each and there is a coloring with . In the second part of the paper we give applications of wide colorings in the theory of generalized quantifiers....