TY - JOUR

T1 - Remarks on Tarski's problem concerning (R, +, *, exp)

AU - van den Dries, Lou

PY - 1984/1/1

Y1 - 1984/1/1

N2 - The chapter presents the elementary theory of the structure (R, +), and the results could be extended to the structure (R, +, exp). Some aspects of on (R, +) are reviewed and its usage is inquired. The decidability of Th(R, +) is a nice result in its own right and quite useful in many theoretical decidability questions but has otherwise not been important in settling open problems. Th(R, +·)= theory of real closed fields is useful in proving properties of real closed fields: in certain cases the only known proof consists of first establishing the property for the field of reals by transcendental methods and then invoking elimination of quantifiers for (R, <,0, 1, +·). This is called Tarski's Principle.

AB - The chapter presents the elementary theory of the structure (R, +), and the results could be extended to the structure (R, +, exp). Some aspects of on (R, +) are reviewed and its usage is inquired. The decidability of Th(R, +) is a nice result in its own right and quite useful in many theoretical decidability questions but has otherwise not been important in settling open problems. Th(R, +·)= theory of real closed fields is useful in proving properties of real closed fields: in certain cases the only known proof consists of first establishing the property for the field of reals by transcendental methods and then invoking elimination of quantifiers for (R, <,0, 1, +·). This is called Tarski's Principle.

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U2 - 10.1016/S0049-237X(08)71811-1

DO - 10.1016/S0049-237X(08)71811-1

M3 - Article

AN - SCOPUS:77956967855

VL - 112

SP - 97

EP - 121

JO - Studies in Logic and the Foundations of Mathematics

JF - Studies in Logic and the Foundations of Mathematics

SN - 0049-237X

IS - C

ER -