Martin's Axiom Applied to Existentially Closed Groups.
Model-completeness for sheaves of structures
On -categorical theories of fields
On -categorical theories of abelian groups
A failure of quantifier elimination.
We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
The logic of Rumely's local-global principle.
Schanuel Nullstellensatz for Zilber fields
We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.
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