Revisiting Uniform Computable Categoricity: For the Sixtieth Birthday of Prof. Rod Downey

Miller, Russell

doi:10.1007/978-3-319-50062-1_18

Cited by 5 publications

(1 citation statement)

References 15 publications

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“…The study of this concept could be independently interesting. For example, how it relates to the known concepts of categoricity (see [9], [20]) or whether there is a syntactic description of this concept. In particular, it is easy to see that if a structure A belongs to a uniformly relatively ∆ 0 αcategorical class of structures then it is uniformly boldface ∆ 0 α -categorical (see [21]).…”

Section: On Categoricity Of Scattered Linear Orders Of Constructive R...mentioning

confidence: 99%

On Categoricity of Scattered Linear Orders Of constructive Ranks

Frolov

Zubkov

2023

Preprint

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In this article we investigated the complexity of isomorphisms be-tween scattered linear orders of constructive ranks. We gave the general upperbound and proved that this bound is sharp. Also, we constructed examples show-ing that the categoricity level of a given scattered linear order can be an arbitraryordinal from 3 to the upper bound, except for the case when the ordinal is thesuccessor of a limit ordinal. The existence question of the scattered linear orderswhose categoricity level equals to the successor of a limit ordinal is still open.

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Section: On Categoricity Of Scattered Linear Orders Of Constructive R...mentioning

confidence: 99%

On Categoricity of Scattered Linear Orders Of constructive Ranks

Frolov

Zubkov

2023

Preprint

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On categoricity of scattered linear orders of constructive ranks

Frolov,

Zubkov

2024

Arch. Math. Logic

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The Complexity of Scott Sentences of Scattered Linear Orders

Alvir¹,

Rossegger²

2020

J. symb. log.

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We calculate the complexity of Scott sentences of scattered linear orders. Given a countable scattered linear order L of Hausdorff rank we show that it has a Scott sentence. It follows from results of Ash [2] that for every countable there is a linear order whose optimal Scott sentence has this complexity. Therefore, our bounds are tight. We furthermore show that every Hausdorff rank 1 linear order has an optimal or Scott sentence and give a characterization of those linear orders of rank with optimal Scott sentences. At last we show that for all countable the class of Hausdorff rank linear orders is complete and obtain analogous results for index sets of computable linear orders.

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Revisiting Uniform Computable Categoricity: For the Sixtieth Birthday of Prof. Rod Downey

Cited by 5 publications

References 15 publications

On Categoricity of Scattered Linear Orders Of constructive Ranks

On Categoricity of Scattered Linear Orders Of constructive Ranks

On categoricity of scattered linear orders of constructive ranks

The Complexity of Scott Sentences of Scattered Linear Orders

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