Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Matthew Harrison-Trainor"'
Publikováno v:
Proceedings of the American Mathematical Society. 149:3999-4013
A recent thread in computable structure theory has been the investigation of computable structures after relativizing, the key idea being that facts which are true for algebraic/structural reasons tend to relativize. On the other hand, there are path
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8cc4ecdffeaff3de55a1085539b03871
https://doi.org/10.1090/proc/15471
https://doi.org/10.1090/proc/15471
Publikováno v:
The Journal of Symbolic Logic. 86:1706-1720
We define the Scott complexity of a countable structure to be the least complexity of a Scott sentence for that structure. This is a finer notion of complexity than Scott rank: it distinguishes between whether the simplest Scott sentence is $\Sigma _
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9a6354eff0984ec13542d6bc7c7c3288
https://doi.org/10.1017/jsl.2021.4
https://doi.org/10.1017/jsl.2021.4
Publikováno v:
The Journal of Symbolic Logic. 85:1664-1686
We study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::383e0c499dc0c96a6bca28c76f4a98ca
https://doi.org/10.1017/jsl.2020.67
https://doi.org/10.1017/jsl.2020.67
Publikováno v:
The Journal of Symbolic Logic. 87:21-46
Our main result is that there exist structures which cannot be computably recovered from their tree of tuples. This implies that there are structures with no computable copies which nevertheless cannot code any information in a natural/functorial way
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9590bb2e39a2959f3e8d863e6c1ad909
https://doi.org/10.1017/jsl.2019.92
https://doi.org/10.1017/jsl.2019.92
Publikováno v:
The Journal of Symbolic Logic. 85:972-1005
This paper investigates the principles that one must add to Boolean algebra to capture reasoning not only about intersection, union, and complementation of sets, but also about the relative size of sets. We completely axiomatize such reasoning under
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d17e6d3e8dc93cc3e94e8f1d03514245
https://doi.org/10.1017/jsl.2019.67
https://doi.org/10.1017/jsl.2019.67
Publikováno v:
Computability. 9:127-137
A computable structure $\mathcal{A}$ has degree of categoricity $\mathbf{d}$ if $\mathbf{d}$ is exactly the degree of difficulty of computing isomorphisms between isomorphic computable copies of $\mathcal{A}$. Fokina, Kalimullin, and Miller showed th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9faf8ce17870d57905c294d30d9b7ef
https://doi.org/10.3233/com-190254
https://doi.org/10.3233/com-190254
Publikováno v:
The Journal of Symbolic Logic
The Journal of Symbolic Logic, Association for Symbolic Logic, 2021, pp.1-20. ⟨10.1017/jsl.2021.58⟩
The Journal of Symbolic Logic, Association for Symbolic Logic, 2021, pp.1-20. ⟨10.1017/jsl.2021.58⟩
The $\Omega $ numbers—the halting probabilities of universal prefix-free machines—are known to be exactly the Martin-Löf random left-c.e. reals. We show that one cannot uniformly produce, from a Martin-Löf random left-c.e. real $\alpha $ , a un
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b961baf1b147d91e7d66512e916e11a
http://arxiv.org/abs/2111.01472
http://arxiv.org/abs/2111.01472
Publikováno v:
Computability. 8:359-375
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3c4e8499a551a8ed6c6d6f93415166ff
https://doi.org/10.3233/com-180101
https://doi.org/10.3233/com-180101
Autor:
Matthew Harrison-Trainor, Meng-Che Ho
Publikováno v:
Proceedings of the American Mathematical Society. 147:3533-3545
An abelian group A A is said to be cancellable if whenever A ⊕ G A \oplus G is isomorphic to A ⊕ H A \oplus H , G G is isomorphic to H H . We show that the index set of cancellable rank 1 torsion-free abelian groups is Π 4 0 \Pi ^0_4 m m -comple
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c929cb990163f136ec471b5d83a9d18f
https://doi.org/10.1090/proc/14546
https://doi.org/10.1090/proc/14546