Search Results - Higher-type and set recursion theory

The Hereditary Partial Effective Functionals and Recursion Theory in Higher Types

Authors: Longo, G. Moggi, E.

Source: The Journal of Symbolic Logic, 1984 Dec 01. 49(4), 1319-1332.

Access URL: https://www.jstor.org/stable/2274281

On church's formal theory of functions and functionals: On Church's formal theory of functions and functionals. The \(\lambda\)- calculus: Connections to higher type recursion theory, proof theory, category theory

Authors: Giuseppe Longo

Source: Annals of Pure and Applied Logic. 40:93-133

Subject Terms: Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations, Logic, bibliography, 0102 computer and information sciences, Functionals in proof theory, higher type recursion theory, proof theory, 16. Peace & justice, 01 natural sciences, \(\lambda\)-calculus, category theory, Higher-type and set recursion theory, Combinatory logic and lambda calculus, survey, 0101 mathematics, semantics, Categorical logic, topoi

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Access URL: https://hal.archives-ouvertes.fr/hal-03318238v1
http://www.sciencedirect.com/science/article/pii/0168007288900176
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https://hal-ens.archives-ouvertes.fr/hal-03318238/document
https://dblp.uni-trier.de/db/journals/apal/apal40.html#Longo88

Equivalence of Some Definitions of Recursion in a Higher Type Object

Authors: Lowenthal, F.

Source: The Journal of Symbolic Logic, 1976 Jun 01. 41(2), 427-435.

Access URL: https://www.jstor.org/stable/2272241

Power set recursion

Authors: Lawrence S. Moss

Source: Annals of Pure and Applied Logic. 71:247-306

Subject Terms: power admissibility, Higher-type and set recursion theory, Logic, semirecursivity, power degree, power set recursion, 0102 computer and information sciences, relativization, 0101 mathematics, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc

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Access URL: https://zbmath.org/736433
https://doi.org/10.1016/0168-0072(94)00005-n
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https://www.sciencedirect.com/science/article/abs/pii/016800729400005N
http://ci.nii.ac.jp/ncid/BA24686497
https://doi.org/10.1016/0168-0072(94)00005-N
https://www.sciencedirect.com/science/article/pii/016800729400005N

Higher type recursion, ramification and polynomial time

Authors: Karl-Heinz Niggl Helmut Schwichtenberg Stephen J. Bellantoni

Source: Annals of Pure and Applied Logic. 104:17-30

Subject Terms: Complexity of computation (including implicit computational complexity), Proof theory in general (including proof-theoretic semantics), polynomial-time computable functions, ramified recursion, Logic, Theory of programming languages, Ramified recursion, Normalisation, higher type recursion, lambda calculus, Higher type recursion, 0102 computer and information sciences, Functionals in proof theory, 01 natural sciences, Recursive functions and relations, subrecursive hierarchies, normalisation, Higher-type and set recursion theory, Polynomial time, Grammars and rewriting systems, Combinatory logic and lambda calculus, Complexity classes (hierarchies, relations among complexity classes, etc.), 0101 mathematics, Second- and higher-order arithmetic and fragments, Lambda calculus

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Access URL: https://philpapers.org/rec/BELHTR
https://dblp.uni-trier.de/db/journals/apal/apal104.html#BellantoniNS00
https://doi.org/10.1016/S0168-0072(00)00006-3
https://www.sciencedirect.com/science/article/pii/S0168007200000063

Turing cones and set theory of the reals

Authors: Löwe, B.

Source: Archive for Mathematical Logic. 40:651-664

Subject Terms: Determinacy principles, Higher-type and set recursion theory, Blackwell determinacy, Other Turing degree structures, Continuum hypothesis and Martin's axiom, 0101 mathematics, Descriptive set theory, 01 natural sciences, Turing determinacy, Turing reducibility

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Access URL: https://zbmath.org/1982455
https://doi.org/10.1007/s001530100092
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https://doi.org/10.1007/s001530100092
https://link.springer.com/article/10.1007/s001530100092
https://core.ac.uk/display/85822423
https://dblp.uni-trier.de/db/journals/aml/aml40.html#Lowe01
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Syntax and semantics in higher-type recursion theory

Authors: David P. Kierstead

Source: Transactions of the American Mathematical Society. 276:67-105

Subject Terms: Higher-type and set recursion theory, generalized computation tree, 4. Education, recursive functional, 0101 mathematics, 16. Peace & justice, 01 natural sciences

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Access URL: https://www.ams.org/tran/1983-276-01/S0002-9947-1983-0684494-7/S0002-9947-1983-0684494-7.pdf
https://zbmath.org/3797736
https://doi.org/10.2307/1999418
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https://www.ams.org/tran/1983-276-01/S0002-9947-1983-0684494-7/S0002-9947-1983-0684494-7.pdf

Safe recursion with higher types and BCK-algebra

Authors: Martin Hofmann

Source: Annals of Pure and Applied Logic. 104:113-166

Subject Terms: BCK-algebras, BCI-algebras, Complexity of computation (including implicit computational complexity), Realisability, Higher-type and set recursion theory, Logic, Polynomial time, Semantics in the theory of computing, Type systems, 0102 computer and information sciences, 0101 mathematics, Functional programming and lambda calculus, 01 natural sciences, Bellantoni-Cook's function algebra

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Access URL: https://zbmath.org/1501504
https://doi.org/10.1016/s0168-0072(00)00010-5
https://www.sciencedirect.com/science/article/abs/pii/S0168007200000105
https://www.sciencedirect.com/science/article/pii/S0168007200000105
https://doi.org/10.1016/S0168-0072(00)00010-5
https://dblp.uni-trier.de/db/journals/apal/apal104.html#Hofmann00

𝛽-recursion theory: \(\beta\)-recursion theory

Authors: Sy-David Friedman

Source: Transactions of the American Mathematical Society. 255:173-200

Subject Terms: 0301 basic medicine, 03 medical and health sciences, Higher-type and set recursion theory, beta- recursion theory, 0101 mathematics, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc, priority arguments, fine structure, cofinality, limit ordinals

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Access URL: https://www.ams.org/tran/1979-255-00/S0002-9947-1979-0542876-7/S0002-9947-1979-0542876-7.pdf
https://zbmath.org/3677822
https://doi.org/10.2307/1998171
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https://www.ams.org/tran/1979-255-00/S0002-9947-1979-0542876-7/

A relation among the higher type recursion theory, the Kleene recursion theory and the common recursion theory

Authors: Sui, Yuefei

Subject Terms: higher-type recursion theory, Higher-type and set recursion theory, functionals, operators, hierarchy, Hierarchies of computability and definability

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Access URL: https://zbmath.org/4118355

Axiomatic recursion theory and the continuous functionals

Authors: Simon Thompson

Source: Journal of Symbolic Logic. 50:442-450

Subject Terms: Higher-type and set recursion theory, Kleene computations, higher type computation theory, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, countable recursion, 15. Life on land, Abstract and axiomatic computability and recursion theory, 01 natural sciences

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Access URL: https://zbmath.org/3946117
https://doi.org/10.2307/2274232
https://projecteuclid.org/handle/euclid.jsl/1183741850
https://www.jstor.org/stable/2274232
http://projecteuclid.org/handle/euclid.jsl/1183741850
https://dblp.uni-trier.de/db/journals/jsyml/jsyml50.html#Thompson85

Higher Recursion Theory And Set Theory

Authors: James Cummings Andrew Marks Yue Yang et al.

Resource Type: eBook.

Subjects: Recursion theory, Set theory

Categories: MATHEMATICS / Set Theory, MATHEMATICS / Logic

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

Recursion theoretic operators and morphisms on numbered sets

Authors: Barendregt, H.P. Longo, G.

Source: Fundamenta Mathematicae, 119, 1, pp. 49-62

Subject Terms: type 2 computability, Canonical numberings, partial operators, 16. Peace & justice, continuity, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc, computable operators on type 2 sets, Higher-type and set recursion theory, Turing operators, Other degrees and reducibilities in computability and recursion theory, Cantor's topology, 0101 mathematics, Scott's topology, Theory of numerations, effectively presented structures, enumeration operators, complete partial orders

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/103922?download.pdf
https://zbmath.org/3873312
https://doi.org/10.4064/fm-119-1-49-62
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https://repository.ubn.ru.nl//bitstream/handle/2066/17252/13269.pdf
http://hdl.handle.net/2066/17252

A Jump Operator in Set Recursion: A jump operator in set recursion

Authors: Dag Normann

Source: Mathematical Logic Quarterly. 25:251-264

Subject Terms: higher-type recursion theory, Higher-type and set recursion theory, computation theory, superjump, set recursion, envelope, 0101 mathematics, Abstract and axiomatic computability and recursion theory, section, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc

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Access URL: https://www.duo.uio.no/bitstream/10852/43970/3/1977-11.pdf
https://www.duo.uio.no/handle/10852/43970

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

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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
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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

1-Generic degrees and minimal degrees in higher recursion theory: 1-generic degrees and minimal degrees in higher recursion theory. II

Authors: Chitat Chong

Source: Japanese journal of mathematics. New series. 13:381-392

Subject Terms: Higher-type and set recursion theory, Logic, admissible ordinals, minimal degree, 1-generic set, 0101 mathematics, 1-generic degree, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc, inadmissible ordinals

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Access URL: https://www.jstage.jst.go.jp/article/math1924/13/2/13_2_381/_pdf
https://zbmath.org/4019045
https://doi.org/10.1016/0168-0072(86)90068-0
https://zbmath.org/4041900
http://ci.nii.ac.jp/naid/130001555336

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

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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

Models for recursion theory

Authors: Dag Normann Johan Moldestad

Source: Journal of Symbolic Logic. 41:719-729

Subject Terms: Higher-type and set recursion theory, Model theory, 0101 mathematics, 16. Peace & justice, 01 natural sciences

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https://doi.org/10.2307/2272391
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Type 2 recursion theory

Authors: Klaus Weihrauch

Source: Theoretical Computer Science. 38:17-33

Subject Terms: computability, Higher-type and set recursion theory, 0102 computer and information sciences, 0101 mathematics, computably open subsets, 01 natural sciences, Computability and recursion theory on ordinals, admissible sets, etc, continuous functions, Theoretical Computer Science, Computer Science(all)

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Access URL: https://core.ac.uk/display/82440448
https://doi.org/10.1016/0304-3975(85)90207-5
https://www.sciencedirect.com/science/article/pii/0304397585902075
https://dblp.uni-trier.de/db/journals/tcs/tcs38.html#Weihrauch85