1. Such real closed fields that are not Archimedean, are non-Archimedean ordered fields . 2. With this identification, the ordered field "'* R "'of hyperreals is constructed. 3. This is because any square in an ordered field is at least, but. 4. Like all ordered fields that properly include "'R "', this field is non-Archimedean. 5. In fact, it is a very special ordered field : the biggest one. 6. For example, it is not enough to construct an ordered field with infinitesimals. 7. An ordered field necessarily has characteristic 0 since the elements necessarily are all distinct. 8. The notion arose from the theory of ordered groups, ordered fields , and local fields. 9. Conversely, it is known that any weakly o-minimal ordered field must be real closed. 10. Dubois showed in 1967 that the answer is negative in general for ordered fields .
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