Structure of Decidable Locally Finite Varieties:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1989
|
| Series: | Progress in Mathematics
79 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propositions of arithmetic. During the 1930s, in the work of such mathematicians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church proposed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)- i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The determination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A. |
| Physical Description: | 1 Online-Ressource (VIII, 216 p) |
| ISBN: | 9781461245520 9781461289081 |
| DOI: | 10.1007/978-1-4612-4552-0 |
Staff View
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| 500 | |a A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propositions of arithmetic. During the 1930s, in the work of such mathematicians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church proposed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)- i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The determination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A. | ||
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| indexdate | 2024-07-10T01:21:06Z |
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| language | English |
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| spelling | McKenzie, Ralph Verfasser aut Structure of Decidable Locally Finite Varieties by Ralph McKenzie, Matthew Valeriote Boston, MA Birkhäuser Boston 1989 1 Online-Ressource (VIII, 216 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 79 A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [1931] paper on formally undecidable propositions of arithmetic. During the 1930s, in the work of such mathematicians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church proposed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)- i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The determination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A. Mathematics Algebra General Algebraic Systems Mathematik Varietät Mathematik (DE-588)4325475-5 gnd rswk-swf Lokal endliche gleichungsdefinierte Klasse (DE-588)4228339-5 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Entscheidbarkeit (DE-588)4152398-2 gnd rswk-swf Lokal endliche gleichungsdefinierte Klasse (DE-588)4228339-5 s Entscheidbarkeit (DE-588)4152398-2 s 1\p DE-604 Varietät Mathematik (DE-588)4325475-5 s 2\p DE-604 Universelle Algebra (DE-588)4061777-4 s 3\p DE-604 Valeriote, Matthew Sonstige oth Progress in Mathematics 79 (DE-604)BV000004120 79 https://doi.org/10.1007/978-1-4612-4552-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McKenzie, Ralph Structure of Decidable Locally Finite Varieties Progress in Mathematics Mathematics Algebra General Algebraic Systems Mathematik Varietät Mathematik (DE-588)4325475-5 gnd Lokal endliche gleichungsdefinierte Klasse (DE-588)4228339-5 gnd Universelle Algebra (DE-588)4061777-4 gnd Entscheidbarkeit (DE-588)4152398-2 gnd |
| subject_GND | (DE-588)4325475-5 (DE-588)4228339-5 (DE-588)4061777-4 (DE-588)4152398-2 |
| title | Structure of Decidable Locally Finite Varieties |
| title_auth | Structure of Decidable Locally Finite Varieties |
| title_exact_search | Structure of Decidable Locally Finite Varieties |
| title_full | Structure of Decidable Locally Finite Varieties by Ralph McKenzie, Matthew Valeriote |
| title_fullStr | Structure of Decidable Locally Finite Varieties by Ralph McKenzie, Matthew Valeriote |
| title_full_unstemmed | Structure of Decidable Locally Finite Varieties by Ralph McKenzie, Matthew Valeriote |
| title_short | Structure of Decidable Locally Finite Varieties |
| title_sort | structure of decidable locally finite varieties |
| topic | Mathematics Algebra General Algebraic Systems Mathematik Varietät Mathematik (DE-588)4325475-5 gnd Lokal endliche gleichungsdefinierte Klasse (DE-588)4228339-5 gnd Universelle Algebra (DE-588)4061777-4 gnd Entscheidbarkeit (DE-588)4152398-2 gnd |
| topic_facet | Mathematics Algebra General Algebraic Systems Mathematik Varietät Mathematik Lokal endliche gleichungsdefinierte Klasse Universelle Algebra Entscheidbarkeit |
| url | https://doi.org/10.1007/978-1-4612-4552-0 |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT mckenzieralph structureofdecidablelocallyfinitevarieties AT valeriotematthew structureofdecidablelocallyfinitevarieties |