Geodesic
Once more on the direct and inverse limits of retractive spectra
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 60-63

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It is proved that any $\forall\exists$-formula which is true on the inverse limit of retractive spector of algebras is true on the direct limit of this spector. We obtain some consecuences from this allegation relative definable functions.
Keywords: retractive spector, direct and inverse limits, definable functions. 
A. G. Pinus. Once more on the direct and inverse limits of retractive spectra. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 60-63. http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a5/
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[1] A. G. Pinus, “On direct and inverse limits of retractive spectra”, Sib. Math. J., 58:6 (2017), 1067–1070 | DOI | MR | Zbl

[2] Yu. L. Ershov, Decisibility Problems and Constructive Models, Nauka, M., 1980 (in Russian)

[3] A. G. Pinus, “Fragments of functional clones”, Algebra and Logic, 56:4 (2017), 318–323 | DOI | MR | Zbl