The real field with an irrational power function and a dense multiplicative subgroup

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

characterizing the multiplicative group of a real closed field in terms of its divisible maximal subgroup

On the decidability of the real field with a generic power function

We show that the theory of the real field with a generic real power function is decidable, relative to an oracle for the rational cut of the exponent of the power function. We show the existence of generic computable real numbers, hence providing an example of a decidable o-minimal proper expansion of the real field by an analytic function.

Definable Relations in the Real Field with a Distinguished Subgroup of the Unit Circle

We describe definable relations in the real field augmented by a binary relation which is an arbitrary multiplicative group of complex numbers contained in the divisible hull of a finitely generated subgroup of the unit circle. We give a complete axiom system for this structure which admits quantifier elimination down to Boolean combinations od existential formulas of a special

the past hospitalization and its association with suicide attempts and ideation in patients with mdd and comparison with bmd (depressed type) group

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