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A Computable Structure with Non-Standard Computability


We find an example of a computable admissible set whose level of computability is higher than that of the standard model of Peano arithmetic. As a byproduct, we construct a 1-decidable model of an undecidable submodel complete theory.

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Correspondence to V. G. Puzarenko.

Additional information

Russian Text © The Author(s), 2018, published in Matematicheskie Trudy, 2018, Vol. 21, No. 2, pp. 3–60.

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Avdeev, R.R., Puzarenko, V.G. A Computable Structure with Non-Standard Computability. Sib. Adv. Math. 29, 77–115 (2019).

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  • admissible set
  • hyperadmissible set
  • hereditarily finite superstructure
  • recursively saturated model
  • computable model
  • decidable model
  • Σ-reducibility
  • Σ-definability