Computability on the probability measures on the Borel sets of the unit interval

Authors: Klaus Weihrauch

Source: Lecture Notes in Computer Science ISBN: 9783540631651

Subject Terms: Other connections with logic and set theory, computable analysis, Computable operators, Probability measures, 0102 computer and information sciences, Models of computation (Turing machines, etc.), 01 natural sciences, Theoretical Computer Science, Higher-type and set recursion theory, probability measures, Computable analysis, 0101 mathematics, computable operators, Computer Science(all)

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Access URL: https://link.springer.com/chapter/10.1007/3-540-63165-8_174
https://dblp.uni-trier.de/db/conf/icalp/icalp97.html#Weihrauch97
https://link.springer.com/content/pdf/10.1007/3-540-63165-8_174.pdf
http://dblp.uni-trier.de/db/conf/icalp/icalp97.html#Weihrauch97

Effective forcing versus proper forcing

Authors: Gerald E. Sacks

Source: Annals of Pure and Applied Logic. 81:171-185

Subject Terms: Other aspects of forcing and Boolean-valued models, Higher-type and set recursion theory, Logic, effective forcing, \(E\)-closure, 0101 mathematics, locally proper forcing, \(E\)-recursion, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/933094
https://doi.org/10.1016/0168-0072(95)00052-6
https://core.ac.uk/display/82292657
https://www.sciencedirect.com/science/article/pii/0168007295000526
https://doi.org/10.1016/0168-0072(95)00052-6
https://dblp.uni-trier.de/db/journals/apal/apal81.html#Sacks96
https://www.sciencedirect.com/science/article/abs/pii/0168007295000526

Local structure of Rogers semilattices of Σn 0-computable numberings: Local structure of Rogers semilattices of \(\Sigma^0_n\)-computable numberings

Authors: S. Yu. Podzorov

Source: Algebra and Logic. 44:82-94

Subject Terms: computability, arithmetic numbering, Higher-type and set recursion theory, recursively enumerable degree, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Theory of numerations, effectively presented structures

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s10469-005-0010-3
https://link.springer.com/10.1007/s10469-005-0010-3

Real recursive functions and their hierarchy

Authors: Jerzy Mycka, José Félix Costa

Source: Journal of Complexity. 20:835-857

Subject Terms: Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, General purpose analog computer, Recursive functions over the reals, Applied Mathematics, Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.), 0102 computer and information sciences, Models of computation (Turing machines, etc.), 01 natural sciences, Recursive functions and relations, subrecursive hierarchies, Higher-type and set recursion theory, Turing machines and related notions, Analog computation, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/2132589
https://doi.org/10.1016/j.jco.2004.06.001
https://dl.acm.org/doi/10.1016/j.jco.2004.06.001
https://core.ac.uk/display/82189849
https://www.mimuw.edu.pl/~salwicki/PPIM/Article.pdf
https://dblp.uni-trier.de/db/journals/jc/jc20.html#MyckaC04
https://www.sciencedirect.com/science/article/pii/S0885064X04000408
https://www.sciencedirect.com/science/article/abs/pii/S0885064X04000408

A proof-theoretic characterization of the basic feasible functionals

Authors: Thomas Strahm

Source: Theoretical Computer Science. 329:159-176

Subject Terms: Proof theory in general (including proof-theoretic semantics), Proof theory, Basic feasible functionals, 0102 computer and information sciences, proof theory, type-two feasibility, 01 natural sciences, Theoretical Computer Science, Higher-type and set recursion theory, Applicative theories, applicative theories, 0101 mathematics, Type two feasibility, Relative consistency and interpretations, basic feasible functionals, Computer Science(all)

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On the non-sequential nature of the interval-domain model of real-number computation

Authors: Martin Hofmann, Martín Hötzel Escardó, Thomas Streicher

Source: Mathematical Structures in Computer Science. 14:803-814

Subject Terms: parallelism, interval-domain environment, Higher-type and set recursion theory, Continuous lattices and posets, applications, real-number computations, Semantics in the theory of computing, functional programming, 0102 computer and information sciences, Models of computation (Turing machines, etc.), 0101 mathematics, Functional programming and lambda calculus, 01 natural sciences, ddc

File Description: application/xml; application/pdf

Access URL: http://www.cs.bham.ac.uk/~mhe/papers/mscs-mediation.pdf
https://zbmath.org/2147880
https://doi.org/10.1017/s0960129504004360
https://dblp.uni-trier.de/db/journals/mscs/mscs14.html#EscardoHS04
https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/on-the-nonsequential-nature-of-the-intervaldomain-model-of-realnumber-computation/83F13A3BF1BB0F2FF558B9C964BAD5BD
http://www.cs.bham.ac.uk/~mhe/papers/mscs-mediation.pdf
http://dblp.uni-trier.de/db/journals/mscs/mscs14.html#EscardoHS04
https://dialnet.unirioja.es/servlet/articulo?codigo=1053896
http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=260184
https://mediatum.ub.tum.de/1315618

Spaces allowing Type‐2 Complexity Theory revisited: Spaces allowing type-2 complexity theory revisited

Authors: Matthias Schröder

Source: Mathematical Logic Quarterly. 50:443-459

Subject Terms: Complexity of computation (including implicit computational complexity), Higher-type and set recursion theory, Topological spaces and generalizations (closure spaces, etc.), Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Type-2 Theory of Effectivity, complexity theory, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Theory of numerations, effectively presented structures, Topological space, limit space, Constructive and recursive analysis

File Description: application/xml

Access URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.200310111
https://dialnet.unirioja.es/servlet/articulo?codigo=2805596
https://dblp.uni-trier.de/db/journals/mlq/mlq50.html#Schroder04

Type‐2 computability on spaces of integrable functions: Type-2 computability on spaces of integrable functions

Authors: Daren Kunkle

Source: Mathematical Logic Quarterly. 50:417-430

Subject Terms: Complexity of computation (including implicit computational complexity), complexity bounds, 02 engineering and technology, 01 natural sciences, Type-2 theory of effectivity, Higher-type and set recursion theory, Fourier transform, 0202 electrical engineering, electronic engineering, information engineering, convolution, 0101 mathematics, integrable functions, Theory of numerations, effectively presented structures, computable operators, Constructive and recursive analysis

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/mlq/mlq50.html#Kunkle04
https://dialnet.unirioja.es/servlet/articulo?codigo=2805598
https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.200310109

Continuous-time computation with restricted integration capabilities

Authors: Manuel L. Campagnolo

Source: Theoretical Computer Science. 317:147-165

Subject Terms: Differential equations, Complexity of computation (including implicit computational complexity), Recursion theory, recursion theory on the reals, real recursive functions, 0102 computer and information sciences, Continuous-time computation, 01 natural sciences, Theoretical Computer Science, Computational complexity, Higher-type and set recursion theory, Exponential space hierarchy, Numerical integration, Complexity classes (hierarchies, relations among complexity classes, etc.), 0101 mathematics, Computer Science(all)

File Description: application/xml

Hierarchies of total functionals over the reals

Authors: Dag Normann

Source: Theoretical Computer Science. 316:137-151

Subject Terms: functionals of finite types over the reals, Higher-type and set recursion theory, hierarchies, 0202 electrical engineering, electronic engineering, information engineering, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Hierarchies of computability and definability, Theoretical Computer Science, Computer Science(all)

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0304397504000817
https://dblp.uni-trier.de/db/journals/tcs/tcs316.html#Normann04
https://core.ac.uk/display/82091263

On the hierarchy and extension of monotonically computable real numbers: On the hierarchy and extension of monotonically computable real numbers.

Authors: Robert Rettinger, Xizhong Zheng

Source: Journal of Complexity. 19:672-691

Subject Terms: Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Dense hierarchy, Applied Mathematics, monotonically computable real numbers, 0102 computer and information sciences, ω-Monotonically computable real numbers, Monotonically computable real numbers, 01 natural sciences, dense hierarchy, weakly computable real numbers, Higher-type and set recursion theory, recursively approximable real numbers, 0101 mathematics, Constructive and recursive analysis

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0885064X03000669
https://dblp.uni-trier.de/db/journals/jc/jc19.html#RettingerZ03
https://www.sciencedirect.com/science/article/pii/S0885064X03000669
https://doi.org/10.1016/S0885-064X(03)00066-9

Domain theory and differential calculus (functions of one variable)

Authors: Edalat, A, Lieutier, A

Source: Proceedings 17th Annual IEEE Symposium on Logic in Computer Science. :277-286

Subject Terms: Logic in computer science, domain-theoretic framework for differential calculus, real-valued functions of a real variable, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, data type for solving differential equations, integration, differentiation, 0102 computer and information sciences, 01 natural sciences, Picard's theorem, Higher-type and set recursion theory, Continuous lattices and posets, applications, 0101 mathematics, Constructive real analysis, data type for differentiable functions, Constructive and recursive analysis

File Description: application/xml

Access URL: http://spiral.imperial.ac.uk/bitstream/10044/1/569/1/Domain%20theory%20and%20differential.pdf
http://dblp.uni-trier.de/db/journals/mscs/mscs14.html#EdalatL04
https://dblp.uni-trier.de/db/journals/mscs/mscs14.html#EdalatL04
https://dialnet.unirioja.es/servlet/articulo?codigo=1053895
https://doi.ieeecomputersociety.org/10.1109/LICS.2002.1029836
https://ieeexplore.ieee.org/document/1029836/
https://spiral.imperial.ac.uk/handle/10044/1/569
https://www.computer.org/csdl/proceedings-article/lics/2002/14830277/12OmNx3HI9S
https://dblp.uni-trier.de/db/conf/lics/lics2002.html#EdalatL02
http://hdl.handle.net/10044/1/569

Second Order Arithmetic and Autonomous Computability: Second order arithmetic and autonomous computability

Authors: E. V. Gailit

Source: Siberian Mathematical Journal. 44:244-249

Subject Terms: models of set theory, Models of arithmetic and set theory, oracle, autonomous numbering, Higher-type and set recursion theory, second-order arithmetic, iterated Kleene computability, 0102 computer and information sciences, set theory without power set axiom, 0101 mathematics, autonomous computability, Second- and higher-order arithmetic and fragments, 01 natural sciences

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Access URL: https://zbmath.org/2047480
https://link.springer.com/article/10.1023/A%3A1022976602764

second order arithmetic and autonomous computability: Second order arithmetic and autonomous computability

Authors: E. V. Gailit

Source: Siberian Mathematical Journal. 44(2):244-249

Subject Terms: models of set theory, Models of arithmetic and set theory, oracle, autonomous numbering, Higher-type and set recursion theory, second-order arithmetic, iterated Kleene computability, set theory without power set axiom, autonomous computability, Second- and higher-order arithmetic and fragments

File Description: application/xml

Access URL: https://zbmath.org/2047480
https://link.springer.com/article/10.1023/A%3A1022976602764

Representation theorems for transfinite computability and definability

Authors: Dag Normann

Source: Archive for Mathematical Logic. 41:721-741

Subject Terms: Inductive definability, Higher-type and set recursion theory, domain with totality, positive induction, 0102 computer and information sciences, 0101 mathematics, representation theorem, infinite computation, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc

File Description: application/xml

Access URL: https://www.duo.uio.no/bitstream/10852/42952/1/1996-20.pdf
https://link.springer.com/article/10.1007/s001530200137
https://www.duo.uio.no/bitstream/10852/42952/1/1996-20.pdf
https://dblp.uni-trier.de/db/journals/aml/aml41.html#Normann02
https://link.springer.com/content/pdf/10.1007/s001530200137.pdf
https://www.duo.uio.no/handle/10852/42952

Continuity, proof systems and the theory of transfinite computations

Authors: Dag Normann

Source: Archive for Mathematical Logic. 41:765-788

Subject Terms: functional, Inductive definability, domains with totality, Higher-type and set recursion theory, compactness, 0101 mathematics, E-logic, 01 natural sciences, Higher-order logic, type theory, transfinite computation

File Description: application/xml

Access URL: https://www.duo.uio.no/bitstream/10852/10266/1/pm19-96.pdf
https://www.duo.uio.no/bitstream/10852/10266/1/pm19-96.pdf
https://www.duo.uio.no/bitstream/handle/10852/10266/pm19-96.pdf?sequence=1
https://dblp.uni-trier.de/db/journals/aml/aml41.html#Normann02a
https://link.springer.com/article/10.1007%2Fs001530200138
https://www.duo.uio.no/handle/10852/10266
https://link.springer.com/content/pdf/10.1007%2Fs001530200138.pdf

In Domain Realizability, not all Functionals on C[–1, 1] are Continuous: In domain realizability, not all functionals on \(C[-1,1]\) are continuous

Authors: Thomas Streicher, Martín Hötzel Escardó

Source: MLQ. 48:41-44

Subject Terms: Categorical semantics of formal languages, continuity principle, functional realizability, Continuous lattices and posets, applications, Higher-type and set recursion theory, realizability over domains, real-valued functions, type 2 effectivity, Constructive and recursive analysis

File Description: application/xml

Access URL: http://www.cs.bham.ac.uk/~mhe/papers/cca2001.pdf
https://zbmath.org/1850713
https://doi.org/10.1002/1521-3870(200210)48:1+<41::aid-malq41>3.0.co;2-v
https://dialnet.unirioja.es/servlet/articulo?codigo=2805308
https://dblp.uni-trier.de/db/journals/mlq/mlq48.html#EscardoS02
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http://onlinelibrary.wiley.com/doi/10.1002/1521-3870%28200210%2948:1+%3C41%3a%3aAID-MALQ41%3E3.0.CO;2-V/abstract

Effectivity in Spaces with Admissible Multirepresentations: Effectivity in spaces with admissible multirepresentations

Authors: Matthias Schröder

Source: MLQ. 48:78-90

Subject Terms: Higher-type and set recursion theory, type-2 theory of effectivity, multirepresentations, Uniform structures and generalizations, weak limit spaces, limit spaces, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), TTE, equilogical spaces, admissibility, sequential topological spaces, Computability and recursion theory on ordinals, admissible sets, etc, Proximity structures and generalizations

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/mlq/mlq48.html#Schroder02
https://dialnet.unirioja.es/servlet/articulo?codigo=2805298

The sequentially realizable functionals

Authors: Longley, John

Source: Longley, J 2002, ' The sequentially realizable functionals ', Annals of Pure and Applied Logic, vol. 117, no. 1-3, pp. 1-93 . https://doi.org/10.1016/S0168-0072(01)00110-5

Subject Terms: Logic, Semantics in the theory of computing, 0102 computer and information sciences, Models of computation (Turing machines, etc.), 01 natural sciences, PCF, realizability, strong stability, Higher-type and set recursion theory, higher-type computability, finite type structures, Combinatory logic and lambda calculus, sequentiality, 0101 mathematics, Theory of numerations, effectively presented structures

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/1838858
https://doi.org/10.1016/s0168-0072(01)00110-5
https://homepages.inf.ed.ac.uk/jrl/Research///srf.pdf
https://link.springer.com/chapter/10.1007/978-3-662-47992-6_11
https://www.sciencedirect.com/science/article/abs/pii/S0168007201001105
https://link.springer.com/content/pdf/10.1007%2F978-3-662-47992-6_11.pdf
https://www.research.ed.ac.uk/portal/files/17651129/1_s2.0_S0168007201001105_main.pdf
https://www.sciencedirect.com/science/article/pii/S0168007201001105
https://www.pure.ed.ac.uk/ws/files/17651129/1_s2.0_S0168007201001105_main.pdf
https://hdl.handle.net/20.500.11820/ffa38503-48ec-4d2d-b441-7fd01a575551

Limit spaces and transfinite types

Authors: Geir Waagb, Dag Normann

Source: Archive for Mathematical Logic. 41:525-539

Subject Terms: Higher-type and set recursion theory, transfinite types, limit spaces, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://philpapers.org/rec/NORLSA
https://link.springer.com/article/10.1007%2Fs001530100131
https://dblp.uni-trier.de/db/journals/aml/aml41.html#NormannW02