I. Kalimullin, A. Melnikov, A. Montalbán. Punctual definability on structures . Annals of Pure and Applied Logic, vol. 172, no. 8 (2021), Paper 102987, 18 pp. - R. Downey, M. Harrison-Trainor, I. Kalimullin, A. Melnikov, D. Turetsky. Graphs are not universal for online computability , Journal of Computer and System Sciences, vol. 112 (2020), pp. 1–12. - N. Greenberg, M. Harrison-Trainor, A. Melnikov, D. Turetsky. Non-density in punctual computability , Annals of Pure and Applied Logic, vol. 172, no. 9 (2021), Paper 102985, 17 pp.

Key Points

• The central aim is to explore punctual definability in mathematical structures and its connections to computability.
• Examined various mathematical structures and their definability.
• Analyzed the characteristics of graphs in relation to online computability.
• Investigated non-density properties within punctual computability.
• Found that punctual definability offers new insights into the nature of definable structures.
• Demonstrated that graphs do not serve as universal models for online computability.
• Identified specific instances of non-density in punctual computability.

Abstract