A structure of punctual dimension two
This paper contributes to the general program which aims to eliminate an unbounded search from proofs and procedures in computable structure theory. A countable structure in a finite language is punctual if its domain is ω and its operations and relations are primitive recursive. A function f is pun...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/152039 |
| _version_ | 1826110853373493248 |
|---|---|
| author | Melnikov, Alexander Ng, Keng Meng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Melnikov, Alexander Ng, Keng Meng |
| author_sort | Melnikov, Alexander |
| collection | NTU |
| description | This paper contributes to the general program which aims to eliminate an unbounded search from proofs and procedures in computable structure theory. A countable structure in a finite language is punctual if its domain is ω and its operations and relations are primitive recursive. A function f is punctual if both f and f⁻¹ are primitive recursive. We prove that there exists a countable rigid algebraic structure which has exactly two punctual presentations, up to punctual isomorphism. |
| first_indexed | 2024-10-01T02:40:58Z |
| format | Journal Article |
| id | ntu-10356/152039 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:40:58Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1520392023-02-28T19:55:31Z A structure of punctual dimension two Melnikov, Alexander Ng, Keng Meng School of Physical and Mathematical Sciences Division of Mathematics Sciences Science::Mathematics Polynomial-time Model-theory This paper contributes to the general program which aims to eliminate an unbounded search from proofs and procedures in computable structure theory. A countable structure in a finite language is punctual if its domain is ω and its operations and relations are primitive recursive. A function f is punctual if both f and f⁻¹ are primitive recursive. We prove that there exists a countable rigid algebraic structure which has exactly two punctual presentations, up to punctual isomorphism. Ministry of Education (MOE) Accepted version The first author was partially supported by the Marsden Foundation of New Zealand. The second author was partially supported by the grants MOE2015-T2-2-055 and RG131/17. 2021-07-30T08:47:24Z 2021-07-30T08:47:24Z 2020 Journal Article Melnikov, A. & Ng, K. M. (2020). A structure of punctual dimension two. Proceedings of the American Mathematical Society, 148(7), 3113-3128. https://dx.doi.org/10.1090/proc/15020 0002-9939 https://hdl.handle.net/10356/152039 10.1090/proc/15020 2-s2.0-85085973627 7 148 3113 3128 en MOE2015-T2-2-055 RG131/17 Proceedings of the American Mathematical Society © 2020 American Mathematical Society. All rights reserved. This paper was published in Proceedings of the American Mathematical Society and is made available with permission of American Mathematical Society. application/pdf |
| spellingShingle | Science::Mathematics Polynomial-time Model-theory Melnikov, Alexander Ng, Keng Meng A structure of punctual dimension two |
| title | A structure of punctual dimension two |
| title_full | A structure of punctual dimension two |
| title_fullStr | A structure of punctual dimension two |
| title_full_unstemmed | A structure of punctual dimension two |
| title_short | A structure of punctual dimension two |
| title_sort | structure of punctual dimension two |
| topic | Science::Mathematics Polynomial-time Model-theory |
| url | https://hdl.handle.net/10356/152039 |
| work_keys_str_mv | AT melnikovalexander astructureofpunctualdimensiontwo AT ngkengmeng astructureofpunctualdimensiontwo AT melnikovalexander structureofpunctualdimensiontwo AT ngkengmeng structureofpunctualdimensiontwo |