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A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

2007; Cambridge University Press; Volume: 72; Issue: 1 Linguagem: Inglês

10.2178/jsl/1174668387

1943-5886

Ehud Hrushovski, Ya’acov Peterzil,

Computability, Logic, AI Algorithms

Abstract We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.