Universal functions and unbounded branching trees
Algebra i logika, Tome 57 (2018) no. 4, pp. 476-491.

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It is proved that a universal $\Sigma$-function exists in a hereditarily finite superstructure over an unbounded branching tree of finite height.
Keywords: hereditarily finite superstructure, unbounded branching tree of finite height, universal $\Sigma$-function.
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A. N. Khisamiev. Universal functions and unbounded branching trees. Algebra i logika, Tome 57 (2018) no. 4, pp. 476-491. http://geodesic.mathdoc.fr/item/AL_2018_57_4_a4/

[1] Yu. L. Ershov, Opredelimost i vychislimost, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996 | MR

[2] V. A. Rudnev, “Ob universalnoi rekursivnoi funktsii na dopustimykh mnozhestvakh”, Algebra i logika, 25:4 (1986), 425–435 | MR | Zbl

[3] Yu. L. Ershov, V. G. Puzarenko, A. I. Stukachev, “$\mathbb{HF}$-Computability”, Computability in context. Computation and logic in the real world, eds. S. B. Cooper et al., Imperial College Press, London, 2011, 169–242 | DOI | MR | Zbl

[4] A. N. Khisamiev, “O $\Sigma$-podmnozhestvakh naturalnykh chisel nad abelevymi gruppami”, Sib. matem. zh., 47:3 (2006), 695–706 | MR | Zbl

[5] A. N. Khisamiev, “$\Sigma$-ogranichennye algebraicheskie sistemy i universalnye funktsii. I”, Sib. matem. zh., 51:1 (2010), 217–235 | MR | Zbl

[6] A. N. Khisamiev, “$\Sigma$-ogranichennye algebraicheskie sistemy i universalnye funktsii. II”, Sib. matem. zh., 51:3 (2010), 676–693 | MR | Zbl

[7] A. N. Khisamiev, “$\Sigma$-odnorodnye algebraicheskie sistemy i $\Sigma$-funktsii. I”, Algebra i logika, 50:5 (2011), 659–684 | MR | Zbl

[8] A. N. Khisamiev, “$\Sigma$-odnorodnye algebraicheskie sistemy i $\Sigma$-funktsii. II”, Algebra i logika, 51:1 (2012), 129–147 | MR | Zbl

[9] A. N. Khisamiev, “Ob universalnoi $\Sigma$-funktsii nad derevom”, Sib. matem. zh., 53:3 (2012), 687–690 | MR | Zbl

[10] A. N. Khisamiev, “Universalnye funktsii i pochti $c$-prostye modeli”, Sib. matem. zh., 56:3 (2015), 663–681 | DOI | MR | Zbl

[11] A. N. Khisamiev, “Ob odnom klasse $c$-prostykh kolets”, Sib. matem. zh., 56:6 (2015), 1416–1426 | DOI | MR

[12] A. N. Khisamiev, “O verkhnei polureshetke Ershova $\mathfrak L_E$”, Sib. matem. zh., 45:1 (2004), 211–228 | MR | Zbl