Open Access Te Herenga Waka-Victoria University of Wellington
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Effective Presentations of Mathematical Structures

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posted on 2024-05-13, 21:22 authored by Marina DorzhievaMarina Dorzhieva

For several algebraic structures, we show that they have a punctual dimension either 1 or ∞. The punctual degree structures of rigid structures and the ordered integers are dense. We consider some classes where every punctual structure from the class can be punctually embedded into its punctual (existential, algebraic) closure. We prove that the space C[0, 1] and the Urysohn space U are computably and punctually universal, and that the Urysohn space is not punctually categorical. And finally, we show that effectively compact punctual presentations of a Stone space are punctually homeomorphically embeddable into Cantor space, and that there is a compact totally disconnected punctual Polish space which is not computably homeomorphically embeddable into Cantor space.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

CC BY-NC 4.0

Degree Discipline


Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Doctor of Philosophy

ANZSRC Socio-Economic Outcome code

280118 Expanding knowledge in the mathematical sciences

ANZSRC Type Of Activity code

1 Pure basic research

Victoria University of Wellington Item Type

Awarded Doctoral Thesis



Victoria University of Wellington School

School of Mathematics and Statistics


Melnikov, Alexander