Abstract
By RCA0, we denote a subsystem of second order arithmetic based on Δ10 comprehension and ∑1 0 induction. We show within this system that the real number system ℝ satisfies all the theorems (possibly with non-standard length) of the theory of real closed fields under an appropriate truth definition. This enables us to develop linear algebra and polynomial ring theory over real and complex numbers, so that we particularly obtain Hilbert's Nullstellensatz in RCA0.
Original language | English |
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Pages (from-to) | 337-349 |
Number of pages | 13 |
Journal | Archive for Mathematical Logic |
Volume | 43 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2004 Apr 1 |
Keywords
- Algebraically closed fields
- Hilbert's Nullstellensatz
- Real closed fields
- Reverse mathematics
- Second order arithmetic
ASJC Scopus subject areas
- Philosophy
- Logic