Geodesic
$\Sigma$-presentations of the ordering on the reals
Algebra i logika, Tome 53 (2014) no. 3, pp. 340-371

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We prove the nonexistence of universal $\Sigma$-presentable linear orderings as well as the effective infinity of the class of $\Sigma$-presentations of the natural order on $\mathbb R$ over an admissible set $\mathbb{HF(R)}$.
Keywords: $\Sigma$-presentation, ordering on reals
Mots-clés : admissible set. 
@article{AL_2014_53_3_a3,
     author = {A. S. Morozov},
     title = {$\Sigma$-presentations of the ordering on the reals},
     journal = {Algebra i logika},
     pages = {340--371},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_3_a3/}
}
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A. S. Morozov. $\Sigma$-presentations of the ordering on the reals. Algebra i logika, Tome 53 (2014) no. 3, pp. 340-371. http://geodesic.mathdoc.fr/item/AL_2014_53_3_a3/