A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Computable isomorphisms, degree spectra of relations, and Scott families

1998
*
Annals of Pure and Applied Logic
*

*Of*course, the finite components are again

*isomorphic*by the existence

*of*

*isomorphisms*at each stage. 2 Claim 7. The

*relation*P is

*computable*. Proof

*of*Claim 7. ... A 0

*and*A 1 are

*isomorphic*. Proof

*of*Claim 6. It is immediate from the construction that A 0,t

*and*A 1,t are

*isomorphic*for every t. ... There has been an extensive study

*of*the

*degree*

*spectra*

*of*

*relations*on

*computably*structures

*and*

*related*results. ...

##
###
Automorphism Groups of Substructure Lattices of Vector Spaces in Computable Algebra
[chapter]

2016
*
Lecture Notes in Computer Science
*

Harizanov,

doi:10.1007/978-3-319-40189-8_26
fatcat:2p5s2kf5xzfwfdf7zakfx43mpy
*and*A. Shlapentokh, "Turing*degrees**of**isomorphism*types*of*geometric objects,"*Computability*3 (2014), pp. 105-134. 54. E. Fokina, V. Harizanov,*and*A. ... Harizanov,*and*D. Turetsky, "*Computability*-theoretic categoricity*and**Scott**families*," 25 pages, submitted. 61. J. Chubb, M. Dabkowski,*and*V. ... Harizanov, "*Degree**spectra**of*the successor*relation*on*computable*linear orderings," Archive for Mathematical Logic 48 (2009), pp. 7-13. 38. D. Cenzer, V. Harizanov,*and*J. ...##
###
Page 4450 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
*
Mathematical Reviews
*

M.] (1-CRNL; Ithaca, NY); Shore, Richard A. (1-CRNL; Ithaca, NY)

*Computable**isomorphisms*,*degree**spectra**of**relations*,*and**Scott**families*. (English summary)*Computability*theory. Ann. Pure Appl. ... Summary: “The spectrum*of*a*relation*R on a*computable*struc- ture W is the set*of*Turing*degrees**of*the image*of*R under all*isomorphisms*between W*and*any other*computable*structure &. ...##
###
Degrees of categoricity on a cone
[article]

2015
*
arXiv
*
pre-print

We investigate the complexity

arXiv:1506.03066v1
fatcat:fq3sau4ubngd7cxonokut44mra
*of**isomorphisms**of**computable*structures on cones in the Turing*degrees*. ... We also show that, for any fixed*computable*structure, there is an ordinal α*and*a cone in the Turing*degrees*such that the exact complexity*of**computing*an*isomorphism*between the given structure*and*... Let e be such that: (1) A is e-*computable*,*and*e*computes*a*Scott**family*for A in which each tuple satisfies a unique formula*and*also*computes*, for tuples in A, which formula in the*Scott**family*they ...##
###
DEGREES OF CATEGORICITY ON A CONE VIA η-SYSTEMS

2017
*
Journal of Symbolic Logic (JSL)
*

We investigate the complexity

doi:10.1017/jsl.2016.43
fatcat:tc7ogdc67bg6hggr6lcpcptgzu
*of**isomorphisms**of**computable*structures on cones in the Turing*degrees*. ... We also show that, for any fixed*computable*structure, there is an ordinal α*and*a cone in the Turing*degrees*such that the exact complexity*of**computing*an*isomorphism*between the given structure*and*... Let e be such that: (i) A*and*η are e-*computable*,*and*e*computes*a*Scott**family*for A in which each tuple satisfies a unique formula*and*also*computes*, for tuples in A, which formula in the*Scott**family*...##
###
Page 3186 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

(NZ-VCTR-SMC; Wellington)

*Degree**spectra**of**relations*on*computable*structures in the presence*of*A*isomorphisms*. (English summary) J. Symbolic Logic 67 (2002), no. 2, 697-720. ... The*computable*dimension*of*a*computable*structure is the num- ber*of*different*computable**isomorphism*classes within the clas- sical*isomorphism*class (that is, the number*of*non-*isomorphic**computable*...##
###
Theory spectra and classes of theories

2017
*
Transactions of the American Mathematical Society
*

We analyze the

doi:10.1090/tran/6917
fatcat:a426jwuld5bizpjhuwfbxxwpj4
*spectra**of*theories that are ω-stable, theories whose*spectra*include almost every*degree*,*and*theories with uniformly arithmetical n-quantifier fragments. ... In addition, we give examples*of*theory*spectra*that contain almost every*degree*, including ones that are known not to be structure*spectra*. ...*of**Scott*sets containing every arithmetical*degree*. ...##
###
An introduction to the Scott complexity of countable structures and a survey of recent results
[article]

2020
*
arXiv
*
pre-print

Such a sentence is called a

arXiv:2011.03923v1
fatcat:ebrlfwondnfhrp35ebqetymggi
*Scott*sentence,*and*can be thought*of*as a description*of*the structure. ... The least complexity*of*a*Scott*sentence for a structure can be thought*of*as a measurement*of*the complexity*of*describing the structure. ... Let F G be the class*of*free groups. ...##
###
An Introduction to the Scott Complexity of Countable Structures and a Survey of Recent Results

2021
*
Bulletin of Symbolic Logic
*

Such a sentence is called a

doi:10.1017/bsl.2021.62
fatcat:miy6gyratjdlflwar52e2c7tyq
*Scott*sentence,*and*can be thought*of*as a description*of*the structure. ... The least complexity*of*a*Scott*sentence for a structure can be thought*of*as a measurement*of*the complexity*of*describing the structure. ...*Scott**spectra*The results*of*this section were proved using the notion*of**Scott*rank defined using symmetric back-*and*-forth*relations*(as in Definition 2.5) except with arbitrary tuples, replacing (2) ...##
###
Computability-Theoretic Complexity of Countable Structures

2002
*
Bulletin of Symbolic Logic
*

*Computable*model theory, also called effective or recursive model theory, studies algorithmic properties

*of*mathematical structures, their

*relations*,

*and*

*isomorphisms*. ... One

*of*the major tasks

*of*

*computable*model theory is to obtain, whenever possible,

*computability*-theoretic versions

*of*various classical model-theoretic notions

*and*results. ... Slaman [76]

*and*Wehner [80] have independently constructed examples

*of*Turing

*degree*

*spectra*

*of*structures consisting

*of*all nonzero Turing

*degrees*. This is not always the case. ...

##
###
Computability-Theoretic Complexity of Countable Structures

2002
*
Bulletin of Symbolic Logic
*

Slaman [76]

doi:10.2307/797952
fatcat:lvanuu567rdefjo7zcepr4t3te
*and*Wehner [80] have independently constructed examples*of*Turing*degree**spectra**of*structures consisting*of*all nonzero Turing*degrees*. This is not always the case. ... Thus, a linear order that is not*isomorphic*to a*computable*one, does not have a*degree**of*its*isomorphism*type. ...##
###
Page 576 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

.%

*and*a new recursive*relation*R on A. By definition, the*degree*spectrum*of*R on &%, S(R), is the set*of*Turing*degrees**of*the images*of*R under the*isomorphisms*that send . to recursive models. ... There is a natural definition*of**computability**of*a*family**of*problems 2 = (Ro, Ri, ---) on M. ...##
###
Calibrating Computational Complexity via Definability: The Work of Julia F. Knight

2022
*
Notices of the American Mathematical Society
*

The author is very grateful for Knight's ongoing mentorship, collaboration,

doi:10.1090/noti2436
fatcat:6g2qjctksnd7plspwz7ysetjpa
*and*friendship,*and*her assistance in putting together this article. ... The second approach is syntactic,*relating*to*Scott*sentences*and**Scott**families*. In this approach, an effective characterization*of*𝒦 is a*computable*infinitary definition*of*𝒦 𝑐 , if any exists. ... In a standard proof*of*the*Scott**Isomorphism*Theorem, one first shows that there is a*Scott**family*for the given structure 𝒜*and*an ordinal 𝛼 in which the definitions*of*all orbits*of*tuples in 𝒜 are ...##
###
Degree spectra and computable dimensions in algebraic structures

2002
*
Annals of Pure and Applied Logic
*

This allows us to show that several theorems about

doi:10.1016/s0168-0072(01)00087-2
fatcat:sksasinkqrhihnq44on2wqq4dy
*degree**spectra**of**relations*on*computable*structures, nonpreservation*of**computable*categoricity,*and**degree**spectra**of*structures remain true when we ... However, this can be an unnecessary duplication*of*effort,*and*lacks generality. ...*and**degree**spectra**of**relations*. ...##
###
Point degree spectra of represented spaces
[article]

2017
*
arXiv
*
pre-print

The notion

arXiv:1405.6866v4
fatcat:tdfa75abczedvnoczicrlxq6yy
*of*point*degree*spectrum creates a connection among various areas*of*mathematics including*computability*theory, descriptive set theory, infinite dimensional topology*and*Banach space theory ... We introduce the point*degree*spectrum*of*a represented space as a substructure*of*the Medvedev*degrees*, which integrates the notion*of*Turing*degrees*, enumeration*degrees*, continuous*degrees*,*and*so on ... The authors are also grateful to Masahiro Kumabe, Joseph Miller, Luca Motto Ros, Philipp Schlicht,*and*Takamitsu Yamauchi for their insightful comments*and*discussions. ...
« Previous

*Showing results 1 — 15 out of 390 results*