We prove that if an ∀∃-formula is true on the inverse limit of the retractive spectrum of algebras, then it is also true on the direct limit and establish some consequences for functions definable on these limits.
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A. G. Pinus, “Fragments of functional clones,” Algebra Logic 56, No. 4, 318–323 (2017).
Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 18, No. 3, 2018, pp. 60-63.
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Pinus, A.G. On Direct and Inverse Limits of Retractive Spectra Once Again. J Math Sci 253, 444–447 (2021). https://doi.org/10.1007/s10958-021-05240-6