This paper presents a decision procedure for a certain class of sentences of first order logic involving integral polynomials and a certain specific analytic transcendental function trans(x) in which the variables range over the real numbers. The list of transcendental functions to which our decision method directly applies includes exp(x), the exponential function with respect to base e, ln(x)...

Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν − , ν+). In this note, we show that there are ending laminations ν+ such that for any choice of ν − , the punctured torus group is transcendental as a subgroup of PSL2C.

How come that finite language can produce certainty — at least a sufficiently certain certainty, sometimes apodictic — in the presence of infinity? The answer can by no means be found in external reality, quite the contrary: it seems that the very purpose of semantics is to make this question untractable with the help of an ad hoc analytical newspeak in which one cannot even formulate the above...

The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of certain known transcendental differential functions, as of Γ(x). Furthermore, it also determines differential transcendency of solution of some functional equatio...

DISCLAIMER: This is just a draft. I am not sure of the final purpose of this document, so at the moment I have included lots of known results, in particular proofs of the usual Fundamental Theorem of Galois theory (in the finite and then the algebraic case). Seeing such proofs helps (me) to understand the analogies between the Fundamental Theorem presented here and the usual cases. Also, CAVEAT...

In this paper we show how the restriction of the complex algebraic cycles to real part of a complex algebraic set îs related to the real algebraic cycles of the real part As a corollary we give examples of smooth submanifolds of a Euchdean space which can not be isotoped to real parts of complex nonsingular subvaneties in the corresponding projective space Algebraic numbers are dense in R. The ...