On recursively saturated models of arithmetic -- A note on existentially complete division rings -- Ideals of integers in nonstandard number fields -- Categories of local functors -- Impredicativity of the existence of the largest divisible subgroup of an Abelian p-group -- Elementary equivalence classes of generic structures and existentially complete structures -- The number of equivalence classes of existentially complete structures -- Finite forcing and generic filters in arithmetic -- Dense embeddings I: A theorem of Robinson in a general setting -- New facts about Hilbert's seventeenth problem -- Nonstandard aspects of Hilbert's irreducibility theorem -- Projective model theory and coforcing -- On algebraic curves over commutative regular rings -- Existence of rigid-like families of Abelian p-groups -- The complexity of Tf and omitting types in FT -- Model-completeness and skolem expansions