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A note on the pp conjecture for sheaves of spaces of orderings

Paweł Gładki (2016)

Communications in Mathematics

In this note we provide a direct and simple proof of a result previously obtained by Astier stating that the class of spaces of orderings for which the pp conjecture holds true is closed under sheaves over Boolean spaces.

A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.

Laureano González-Vega, Henri Lombardi (1992)

Extracta Mathematicae

Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...

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