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Turing degrees of isomorphism types of geometric objects
[article]

2011
*
arXiv
*
pre-print

In particular, we show that any

arXiv:1106.2763v2
fatcat:d72o3ztqjjemzonwkvjclr2skq
*Turing**degree*may occur as the least*degree**of*an*isomorphic*copy*of*a structure*of*these kinds. We also show that these structures may fail to have a least*degree*. ... We initiate the computability-theoretic study*of*ringed spaces and schemes. ... Then for any*Turing**degree*d, there is a member*of*C whose*isomorphism**type*has*Turing**degree*d. There is also a member*of*C whose*isomorphism**type*has no*Turing**degree*. ...##
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A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS

2018
*
Journal of Symbolic Logic (JSL)
*

AbstractFried and Kollár constructed a fully faithful functor from the category

doi:10.1017/jsl.2017.50
fatcat:juoiknhs3bbvta5mfydwvcop3e
*of*graphs to the category*of*fields. ... a countable field ${\cal F}$*of*arbitrary characteristic with the same essential computable-model-theoretic properties as ${\cal S}$. ... The*degree*spectrum DgSp A (R)*of*a relation R on a computable structure A is the set*of*all*Turing**degrees**of*images*of*R under*isomorphisms*f from A onto computable structures B. ...##
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Automorphism Groups of Substructure Lattices of Vector Spaces in Computable Algebra
[chapter]

2016
*
Lecture Notes in Computer Science
*

Shlapentokh, "

doi:10.1007/978-3-319-40189-8_26
fatcat:2p5s2kf5xzfwfdf7zakfx43mpy
*Turing**degrees**of**isomorphism**types**of**geometric**objects*," Computability 3 (2014), pp. 105-134. 54. E. Fokina, V. Harizanov, and A. ... Harizanov, "Groups with orderings*of*arbitrary algorithmic complexity," 22 pages, accepted for publication in: Sets and Computations (IMS, National University*of*Singapore), R. Dilip, S.D. ... Frederick Nelson, A*Geometric*Approach to Rations*of*π/3-Congruent Numbers, Department*of*Mathematics, PhD, Howard University, 2011. 9. ...##
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Page 1927 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

For these

*types**of*struc- Schoen, R. [Schoen, Richard M.] (1-STF; Stanford, CA);*tures*one has*isomorphisms*between the cotangent bundle and Wolfson, J. (1-MIS; East Lansing, M1) the tangent bundle. ... Edith Padron (E-LALAM-FM;; La Laguna) Lagrangian submanifolds have been important*geometric**objects**of*study in symplectic geometry since its birth. ...##
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Page 2015 of Mathematical Reviews Vol. , Issue 95d
[page]

1995
*
Mathematical Reviews
*

The proof requires only to show that a subvariety S (

*of**degree*d)*of*Y*of*codimension one is a complete intersection*of*Y (*of**degree*m) and a hypersurface*of*P”. ...*of*general*type*with p, > 0 is base-point-free. ...##
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Spaces in mathematics

2018
*
WikiJournal of Science
*

1][details 1] A space consists

doi:10.15347/wjs/2018.002
fatcat:azjykkza4ffmrbson6jnsso7nm
*of*selected mathematical*objects*that are treated as points, and selected relationships between these points. ... While modern mathematics use many*types**of*spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion*of*"space" itself. [ ... A general definition*of*"structure", proposed by Bourbaki [2] , embraces all common*types**of*spaces, provides a general definition*of**isomorphism*, and justifies the transfer*of*properties between*isomorphic*...##
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Page 6211 of Mathematical Reviews Vol. , Issue 97J
[page]

1997
*
Mathematical Reviews
*

Fur- ther, he describes some

*geometrical**objects*invariant with respect to such*isomorphisms*. Josef Janyska (Brno) 97}:53025 53B21 53B20 Zhao, Pei Biao Projectively recurrent Riemannian spaces. ... (RS-NZNV; Nizhnii Novgorod) Trajectory*isomorphisms**of*quasigeodesic flows*of*second*degree*and their invariants. (Russian) Izv. Vyssh. Uchebn. Zaved. ...##
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A Modern Point of View on Anomalies
[article]

2019
*
arXiv
*
pre-print

We review the concept

arXiv:1903.02828v1
fatcat:winn5t4d7nalboje5qgoi6jmgy
*of*anomaly field theory, namely the fact that the anomalies*of*a d-dimensional field theory can be encoded in a d+1-dimensional field theory functor. ... We also sketch the status*of*global anomaly cancellation checks in string theory. This paper is based on a talk given at the Durham Symposium 'Higher Structures in M-theory' in August 2018. ... I would like to thank the organizers*of*the Durham Symposium "Higher Structures in M-theory" for the opportunity to present this work. Key words. ...##
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Page 4683 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

The authors use the so-called Miwa coordinates to reformulate the key

*objects**of*the (algebro-*geometric*) theory*of*the KP hierarchy, such as tau-function, wave function, bilinear identity and addition ... This is a nice survey*of*old and new results related to Arnol’d’s strange duality for 14*isomorphism*classes*of*exceptional uni- modal surface singularities. ...##
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Page 644 of Mathematical Reviews Vol. , Issue 88b
[page]

1988
*
Mathematical Reviews
*

the global fine structure

*of*&,-categorical struc-*tures*. ... The first part*of*the paper concerns the proof*of*the following re- sults: (a) (Fourth*degree*bound) If S C R’ is semialgebraically de- scribable by polynomials fj, ---, fm € R[x1,---,xX,]*of*total*degree*...##
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Page 4496 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

Differential characters can be identified with equivalence classes

*of*various kinds*of**geometric**objects*. For example H? ... If I*(G) is the space*of*invariant polynomials*of**degree*k on the Lie algebra*of*G then the Weil homomorphism /*(G) — H**(BG,R) is an*isomorphism*. ...##
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The Digital and the Real Universe. Foundations of Natural Philosophy and Computational Physics

2019
*
Philosophies
*

This example underlines that modern physics, in the tradition

doi:10.3390/philosophies4010003
fatcat:mgv373e4sbhgreenikab6am5qa
*of*Newton's Principia Mathematica Philosophiae Naturalis, is a further development*of*natural philosophy with the rigorous methods*of*mathematics ... Computational Foundations*of*Mathematics, Science, Technology, and Philosophy." ... Mathematical theories*of*nature are*isomorphic*to mathematical structures*of*different*degrees*and, by that, embedded in the categorical framework*of*mathematics. ...##
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Simple structures with complex symmetry

2010
*
Algebra and Logic
*

We define the automorphism spectrum

doi:10.1007/s10469-010-9079-4
fatcat:6ynpw7jymjehnodcfv2cm7am2y
*of*a computable structure M, a measurement*of*the complexity*of*the symmetries*of*M, and prove that certain sets*of**Turing**degrees*can be realized as automorphism spectra ... , while certain others cannot.*of**degrees*≥ T d, then d is hyperarithmetical. ... this correspondence preserves the*Turing**degree**of*any*isomorphism**of**degree*≥ deg(A). ...##
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Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
[article]

2020
*
arXiv
*
pre-print

In Section 2.1 we describe the

arXiv:2008.09788v2
fatcat:b6v5vptirrgk5fa6rvckojevja
*geometric*equivalence, the elementary equivalence, and the isotypicity*of*algebras. ... In this setting Plotkin's problem on the structure*of*automorphisms*of*(auto)endomorphisms*of*free*objects*, and auto-equivalence*of*categories is pretty natural and important. ... Two algebras are isotypic if the sets*of*realizable*types*over H1 and H2 coincide. So, by some abuse*of*language these algebras have the same logic*of**types*. ...##
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Searching for pharmacophoric patterns in databases of three-dimensional chemical structures

1995
*
Journal of Molecular Recognition
*

*of*the struc-

*tures*passing the screening and

*geometric*searches) but they were also substantially faster in execution. ... Inspection

*of*these hits using molecular graphics software demonstrates a substantial

*degree*

*of*3D overlap with the target struc-

*ture*that would be difficult, if not impossible, to achieve with a simple ...

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