The quantifier complexity of NF.
The Ramsey sets and related sigma algebras and ideals
The range of a planar function with ambiguous points
The rational field is not universally definable in pseudo-exponentiation
We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field.
The rationality of the Poincaré series associated to the p-adic points on a variety.
The real closure of a commutative regular f-ring
The real field with the rational points of an elliptic curve
We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.
The reaping and splitting numbers of nice ideals
We examine the splitting number (B) and the reaping number (B) of quotient Boolean algebras B = (ω)/ℐ where ℐ is an ideal or an analytic P-ideal. For instance we prove that under Martin’s Axiom ((ω)/ℐ) = for all ideals ℐ and for all analytic P-ideals ℐ with the BW property (and one cannot drop the BW assumption). On the other hand under Martin’s Axiom ((ω)/ℐ) = for all ideals and all analytic P-ideals ℐ (in this case we do not need the BW property). We also provide applications of these characteristics...
The recursive sets in certain monadic second order fragments of arithmetic.
The Rediscovery of the Cantor-Dedekind Correspondence.
The regular inverse Galois problem over non-large fields
By a celebrated theorem of Harbater and Pop, the regular inverse Galois problem is solvable over any field containing a large field. Using this and the Mordell conjecture for function fields, we construct the first example of a field over which the regular inverse Galois problem can be shown to be solvable, but such that does not contain a large field. The paper is complemented by model-theoretic observations on the diophantine nature of the regular inverse Galois problem.
The regular open algebra of βRR is not equal to the completion of P(ω)/fin
Two compact spaces are co-absoluteif their respective regular open algebras are isomorphic (i.e. homeomorphic Gleason covers). We prove that it is consistent that βω and βℝ are not co-absolute.
The regularity properties on the real line
The relation of rapid ultrafilters and Q-points to Van der Waerden ideal
The relationship between two weak forms of the axiom of choice
The relative consistency of some consequences of the existence of measurable cardinal numbers [Book]
The resolution tableau for logics of likelihood
The Role of Halaš Identity in Orthomodular Lattices
We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter.
The role of rudimentary relations in complexity theory
The role of the omitting types theorem in infinitary logic.