The notion of a randomization of a first-order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original first-order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete first-order theory is a complete theory in continuous logic that admits elimination of quantifiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable.

Itaï Ben Yaacov ^{1};
H. Jerome Keisler ^{1}

@article{CML_2009__1_2_197_0, author = {Ita{\"\i} Ben Yaacov and H. Jerome Keisler}, title = {Randomizations of models as metric structures}, journal = {Confluentes Mathematici}, pages = {197--223}, publisher = {World Scientific Publishing Co Pte Ltd}, volume = {1}, number = {2}, year = {2009}, doi = {10.1142/S1793744209000080}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744209000080/} }

TY - JOUR AU - Itaï Ben Yaacov AU - H. Jerome Keisler TI - Randomizations of models as metric structures JO - Confluentes Mathematici PY - 2009 SP - 197 EP - 223 VL - 1 IS - 2 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744209000080/ DO - 10.1142/S1793744209000080 LA - en ID - CML_2009__1_2_197_0 ER -

%0 Journal Article %A Itaï Ben Yaacov %A H. Jerome Keisler %T Randomizations of models as metric structures %J Confluentes Mathematici %D 2009 %P 197-223 %V 1 %N 2 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744209000080/ %R 10.1142/S1793744209000080 %G en %F CML_2009__1_2_197_0

Itaï Ben Yaacov; H. Jerome Keisler. Randomizations of models as metric structures. Confluentes Mathematici, Volume 1 (2009) no. 2, pp. 197-223. doi : 10.1142/S1793744209000080. https://cml.centre-mersenne.org/articles/10.1142/S1793744209000080/

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