Geodesic
It is Consistent That There Exists an eta1-ordered Real Closed Field Which is not Hyper-real
Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 17 .

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We provide an example of a model of ZFC in which there exists an $\eta_1$-ordered real closed field which is not a hyper-real field.
Classification : 12J15 03E05 
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     author = {Jadran Stojanovi\'c and \v{Z}ikica Perovi\'c},
     title = {It is {Consistent} {That} {There} {Exists} an eta1-ordered {Real} {Closed} {Field} {Which} is not {Hyper-real}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {17 },
     publisher = {mathdoc},
     volume = {_N_S_61},
     number = {75},
     year = {1997},
     zbl = {0999.12501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a2/}
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Jadran Stojanović; Žikica Perović. It is Consistent That There Exists an eta1-ordered Real Closed Field Which is not Hyper-real. Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 17 . http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a2/