Indiscernibles and satisfaction classes in arithmetic

Authors: Enayat, Ali

Source: Archive for Mathematical Logic. 63:655-677

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, Peano arithmetic, satisfaction classes, indiscernibles, FOS: Mathematics, Mathematics - Logic, 0101 mathematics, Logic (math.LO), Relative consistency and interpretations, 03F30, 03F25, 03C62, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.08411
https://zbmath.org/7874619
https://doi.org/10.1007/s00153-024-00915-8

Sets of real numbers closed under Turing equivalence: applications to fields, orders and automorphisms

Authors: Ongay-Valverde, Iván^{Aff1, Aff2, Aff3, IDs00153023008657_cor1}

Source: Archive for Mathematical Logic. :1-27

Structures interpretable in models of bounded arithmetic

Authors: Neil Thapen

Source: Annals of Pure and Applied Logic. 136:247-266

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, Logic, bounded arithmetic, 0102 computer and information sciences, arithmetic with a top, models of arithmetic, 01 natural sciences, Weak Pigeonhole Principle, Arithmetic with a top, Bounded arithmetic, Complexity classes (hierarchies, relations among complexity classes, etc.), Weak pigeonhole principle, 0101 mathematics

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https://doi.org/10.1016/j.apal.2005.04.005
https://dblp.uni-trier.de/db/journals/apal/apal136.html#Thapen05
https://www.sciencedirect.com/science/article/abs/pii/S0168007205000382
https://www.sciencedirect.com/science/article/pii/S0168007205000382
https://core.ac.uk/display/82524637

Some variations of the Hardy hierarchy

Authors: Bożena Piekart, Henryk Kotlarski

Source: MLQ. 51:417-434

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, quickly growing functions, Partitions of sets, approximation lemma, Cut-elimination and normal-form theorems, 0101 mathematics, Hardy hierarchy, 01 natural sciences

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/mlq/mlq51.html#KotlarskiP05
https://dialnet.unirioja.es/servlet/articulo?codigo=2805524

Computational Structuralism†: Computational structuralism

Authors: Halbach, V, Horsten, LFM

Source: Philosophia Mathematica. 13:174-186

Subject Terms: structuralism, Models of arithmetic and set theory, Philosophy of mathematics, Nonstandard models of arithmetic, 06 humanities and the arts, 0101 mathematics, Philosophical and critical aspects of logic and foundations, models of arithmetic, 0603 philosophy, ethics and religion, Tennenbaum's theorem, 01 natural sciences

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https://doi.org/10.1093/philmat/nki021
https://philpapers.org/rec/HALCSD-2
http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1tea2qdbfb6c44

Fragments of Arithmetic and true sentences

Authors: Cordón Franco, Andrés, Fernández Margarit, Alejandro, Lara Martín, Francisco Félix

Contributors: Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial

Source: idUS. Depósito de Investigación de la Universidad de Sevilla
Universidad de Sevilla (US)
instname

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, 4. Education, \(\Delta_{n+1}\)-formulas, 0101 mathematics, quantifier complexity, 16. Peace & justice, true sentences, 01 natural sciences, fragments of arithmetic, parameter-free schemes

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https://hdl.handle.net/11441/87545
https://idus.us.es/handle//11441/87545
https://dblp.uni-trier.de/db/journals/mlq/mlq51.html#Cordon-FrancoFM05
https://onlinelibrary.wiley.com/doi/pdf/10.1002/malq.200410034
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https://idus.us.es/handle/11441/87545
https://philpapers.org/rec/CORFOA-4

Generic automorphisms and graph coloring

Authors: James H. Schmerl

Source: Discrete Mathematics. 291:235-242

Subject Terms: Recursively saturated, Models of arithmetic and set theory, Coloring of graphs and hypergraphs, Peano Arithmetic, Generic automorphisms, Discrete Mathematics and Combinatorics, Recursively saturated model, 0102 computer and information sciences, 0101 mathematics, Hedetniemi's conjecture, 01 natural sciences, Theoretical Computer Science

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Access URL: https://core.ac.uk/display/82676951
https://dblp.uni-trier.de/db/journals/dm/dm291.html#Schmerl05
https://www.sciencedirect.com/science/article/abs/pii/S0012365X04004145
https://www.sciencedirect.com/science/article/pii/S0012365X04004145

The minimal e-degree problem in fragments of Peano arithmetic

Authors: Arslanov, M.M., Chong, C.T., Cooper, S.B., Yang, Y.

Contributors: MATHEMATICS

Source: SCOPUS01680072-2005-131-13-SID7244226325

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, Logic, \(\Sigma_2\)-collection, e-degrees, Other degrees and reducibilities in computability and recursion theory, fragments of arithemtic, 0101 mathematics, 01 natural sciences

File Description: application/xml

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https://openrepository.ru/article?id=130624
https://core.ac.uk/display/82827520
https://dblp.uni-trier.de/db/journals/apal/apal131.html#ArslanovCCY05
https://philpapers.org/rec/ARSTME
https://www.sciencedirect.com/science/article/pii/S0168007204000910

Blending Set and Interval Arithmetic for Maximal Reliability: Blending set and interval arithmetic for maximal reliability

Authors: J. Vervloet, Annie Cuyt, Brigitte Verdonk

Source: Computing. 74:41-65

Subject Terms: Models of arithmetic and set theory, inclusion property, Interval and finite arithmetic, 0102 computer and information sciences, interval arithmetic, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2162514
https://doi.org/10.1007/s00607-004-0090-2
https://dblp.uni-trier.de/db/journals/computing/computing74.html#VerdonkVC05
https://link.springer.com/article/10.1007/s00607-004-0090-2

Substructure lattices and almost minimal end extensions of models of Peano arithmetic

Authors: James H. Schmerl

Source: Mathematical Logic Quarterly. 50:533-539

Subject Terms: Models of arithmetic and set theory, Peano Arithmetic, almost minimal extension, Nonstandard models of arithmetic, substructure lattice, lattice representations, partition lattices, 0101 mathematics, Representation theory of lattices, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2134244
https://doi.org/10.1002/malq.200310118
https://dialnet.unirioja.es/servlet/articulo?codigo=2805621
https://dblp.uni-trier.de/db/journals/mlq/mlq50.html#Schmerl04

Leibnizian models of set theory

Authors: Enayat, Ali

Source: J. Symbolic Logic 69, iss. 3 (2004), 775-789

Subject Terms: Models of arithmetic and set theory, Leibniz-Mycielski axiom, 03H99, 03C50, 03C62, 0101 mathematics, Leibnizian model, 16. Peace & justice, 01 natural sciences

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Access URL: http://journals.cambridge.org/abstract_S0022481200007623
https://projecteuclid.org/journals/journal-of-symbolic-logic/volume-69/issue-3/Leibnizian-models-of-set-theory/10.2178/jsl/1096901766.full
http://fs2.american.edu/enayat/www/Leib.pdf
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022481200007623
https://dblp.uni-trier.de/db/journals/jsyml/jsyml69.html#Enayat04
http://projecteuclid.org/euclid.jsl/1096901766

Models of set theory with definable ordinals

Authors: Ali Enayat

Source: Archive for Mathematical Logic. 44:363-385

Subject Terms: Models of arithmetic and set theory, Paris models, DO models, Consistency and independence results, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2168087
https://doi.org/10.1007/s00153-004-0256-9
https://dblp.uni-trier.de/db/journals/aml/aml44.html#Enayat05
https://link.springer.com/article/10.1007/s00153-004-0256-9

An incompleteness theorem for βn-models: An incompleteness theorem for \(\beta_n\)-models

Authors: Mummert, Carl, Simpson, Stephen G.

Source: J. Symbolic Logic 69, iss. 2 (2004), 612-616

Subject Terms: Models of arithmetic and set theory, model, second-order arithmetic, Gödel, 0101 mathematics, incompleteness, 16. Peace & justice, Second- and higher-order arithmetic and fragments, Foundations of classical theories (including reverse mathematics), 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/2199948
https://doi.org/10.2178/jsl/1082418545
https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/an-incompleteness-theorem-for-nmodels/C2A6FC4ADE81710207C0896C046FB453
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http://projecteuclid.org/download/pdf_1/euclid.jsl/1082418545
http://projecteuclid.org/euclid.jsl/1082418545

A note on a theorem of Kanovei

Authors: Roman Kossak

Source: Archive for Mathematical Logic. 43:565-569

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, end extensions, Nonstandard models of arithmetic, models of Peano arithmetic, standard systems, Nonstandard arithmetic (number-theoretic aspects), 0101 mathematics, 01 natural sciences, Nonstandard arithmetic and field theory, fragments of arithmetic

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Access URL: https://zbmath.org/2123167
https://doi.org/10.1007/s00153-004-0218-2
https://dblp.uni-trier.de/db/journals/aml/aml43.html#Kossak04
https://link.springer.com/article/10.1007/s00153-004-0218-2
https://rd.springer.com/article/10.1007/s00153-004-0218-2

Undefinability of truth and nonstandard models

Authors: Roman Kossak

Source: Annals of Pure and Applied Logic. 126:115-123

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, satisfaction classes, Logic, Nonstandard arithmetic (number-theoretic aspects), 02 engineering and technology, undefinability of truth, models of arithmetic, recursive saturation, 01 natural sciences, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Nonstandard arithmetic and field theory

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Access URL: https://zbmath.org/2083175
https://doi.org/10.1016/j.apal.2003.10.011
https://www.sciencedirect.com/science/article/pii/S0168007203000964
https://dblp.uni-trier.de/db/journals/apal/apal126.html#Kossak04

The incompleteness theorems after 70 years

Authors: Henryk Kotlarski

Source: Annals of Pure and Applied Logic. 126:125-138

Subject Terms: First-order arithmetic and fragments, Proof theory in general (including proof-theoretic semantics), arithmetized completeness theorem, Models of arithmetic and set theory, satisfaction classes, Logic, Gödel's incompleteness theorems, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2083176
https://doi.org/10.1016/j.apal.2003.10.012

Arithmetical independence results using higher recursion theory

Authors: Arana, Andrew

Source: J. Symbolic Logic 69, iss. 1 (2004), 1-8

Subject Terms: First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, independence, 0202 electrical engineering, electronic engineering, information engineering, Computable structure theory, computable model theory, 02 engineering and technology, 0101 mathematics, models of arithmetic, 16. Peace & justice, 01 natural sciences

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Access URL: https://zbmath.org/2199909
https://doi.org/10.2178/jsl/1080938820
https://dblp.uni-trier.de/db/journals/jsyml/jsyml69.html#Arana04
https://www.jstor.org/stable/pdfplus/30041702.pdf
https://projecteuclid.org/handle/euclid.jsl/1080938820
https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/arithmetical-independence-results-using-higher-recursion-theory/A30325FAE9D00E85FDD464452BF98190
http://projecteuclid.org/euclid.jsl/1080938820

A solution to identities problem in 2‐element HSI‐algebras: A solution to identities problem in 2-element HSI-algebras

Authors: Gurgen Asatryan

Source: Mathematical Logic Quarterly. 50:175-178

Subject Terms: Models of arithmetic and set theory, Nonstandard models of arithmetic, Connections of number theory and logic, Equational classes, universal algebra in model theory, Tarski's high school problem, exponentiation, HSI algebra, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2062675
https://doi.org/10.1002/malq.200310087
http://onlinelibrary.wiley.com/doi/10.1002/malq.200310087/abstract
https://dblp.uni-trier.de/db/journals/mlq/mlq50.html#Asatryan04
https://dialnet.unirioja.es/servlet/articulo?codigo=2805590

On the Leibniz–Mycielski axiom in set theory: On the Leibniz-Mycielski axiom in set theory

Authors: Ali Enayat

Source: Fundamenta Mathematicae. 181:215-231

Subject Terms: Other set-theoretic hypotheses and axioms, Models of arithmetic and set theory, Leibniz-Mycielski axiom, axiom of choice, Axiom of choice and related propositions, 0202 electrical engineering, electronic engineering, information engineering, Consistency and independence results, 02 engineering and technology, 0101 mathematics, identity of indiscernibles, 01 natural sciences

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https://zbmath.org/2120050
https://doi.org/10.4064/fm181-3-2
https://eudml.org/doc/282624
https://www.impan.pl/shop/publication/transaction/download/product/88387?download.pdf
http://journals.impan.pl/cgi-bin/doi?fm181-3-2
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/fundamenta-mathematicae/all/181/3/88387/on-the-leibniz-8211-mycielski-axiom-in-set-theory
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-2

Some combinatorial principles defined in terms of elementary submodels

Authors: Sakaé Fuchino, Stefan Geschke

Source: Fundamenta Mathematicae. 181:233-255

Subject Terms: Other set-theoretic hypotheses and axioms, SEP, Models of arithmetic and set theory, weak Freese-Nation property, Consistency and independence results, almost disjoint number, 0101 mathematics, Cohen model, Other combinatorial set theory, 01 natural sciences, Cardinal characteristics of the continuum

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https://zbmath.org/2120051
https://doi.org/10.4064/fm181-3-3
https://www.impan.pl/shop/publication/transaction/download/product/88388?download.pdf
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