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We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T(M) eliminates quantifiers down to Boolean combinations of certain existential formulas.
We prove that if M is any model of a trivial, strongly minimal theory, then the elementary diagram Th(MM ) is a model complete LM -theory. We conclude that all countable models of a trivial, strong...
Borel complexity of complete, first order theories(status report).
We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly posi...
The family of translation surfaces $(X_g,\omega_g)$ constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus $g$ greater than or equal to $3$. ...
For a sequence of i.i.d. Banach space-valued random variables $\{X_{n}; ~n \geq 1 \}$ and a sequence of positive constants $\{a_{n}; ~n \geq 1 \}$, the relationship between the Baum--Katz--Spitzer com...
Let $ \{X,~X_{n};~n \geq 1 \}$ be a sequence of i.i.d. Banach space valued random variables and let $\{a_{n}; ~n \geq 1 \}$ be a sequence of positive constants such that \[ a_{n} \uparrow \infty ~~\mb...

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