Formal number theory and computability A workbook
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1982
|
| Schriftenreihe: | Oxford logic guides.
7. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV003665279 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 900725s1982 d||| |||| 00||| eng d | ||
| 020 | |a 0198531788 |9 0-19-853178-8 | ||
| 020 | |a 0198531885 |9 0-19-853188-5 | ||
| 035 | |a (OCoLC)8475061 | ||
| 035 | |a (DE-599)BVBBV003665279 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-739 |a DE-19 |a DE-706 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA241 | |
| 082 | 0 | |a 512/.72 |2 19 | |
| 082 | 0 | |a 511.3/076 |2 19 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a 03B30 |2 msc | ||
| 084 | |a 10N05 |2 msc | ||
| 100 | 1 | |a Fisher, Alec |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Formal number theory and computability |b A workbook |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1982 | |
| 300 | |a XIII, 190 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford logic guides. |v 7. | |
| 490 | 0 | |a Oxford science publications. | |
| 650 | 4 | |a Axiomatique | |
| 650 | 4 | |a Calculabilité | |
| 650 | 4 | |a Exercice logique | |
| 650 | 4 | |a Gödel, Théorème de | |
| 650 | 7 | |a Gödel, Théorème de |2 ram | |
| 650 | 7 | |a Incomplétude, Théorèmes d' |2 ram | |
| 650 | 4 | |a Indécidabilité | |
| 650 | 4 | |a Nombres, Théorie des | |
| 650 | 7 | |a Nombres, Théorie des |2 ram | |
| 650 | 4 | |a Théorie nombre | |
| 650 | 4 | |a Théorèmes d'incomplétude | |
| 650 | 7 | |a Wiskundige logica |2 gtt | |
| 650 | 4 | |a Gödel's theorem | |
| 650 | 4 | |a Incompleteness theorems | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Berechenbarkeit |0 (DE-588)4138368-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 1 | 1 | |a Berechenbarkeit |0 (DE-588)4138368-0 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Oxford logic guides. |v 7. |w (DE-604)BV000013997 |9 7. | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002333856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002333856 | ||
Datensatz im Suchindex
| _version_ | 1804118012396044288 |
|---|---|
| adam_text | CONTENTS
Introduction xi
Part I The formalization of number theory 1
1. Proving some basic results 3
Divisibility and primes The Fundamental Theorem of Arithmetic
The Euclidean Algorithm The infinitude of the primes The
Chinese Remainder Theorem Godel s ^ function The question of
elementary methods
2. Eliciting assumptions 13
Eliciting assumptions: a first example A direct proof Reductio
ad absurdum Mathematical induction Excluded middle and
proof by cases — Summary of principles
3. Testing the soundness of logical assumptions 24
Is there a test for soundness? Constructing truth tables The truth
tables A short truth table method Some useful equivalences
Predicate logic
4. Problems in the foundations of mathematics 31
Intuitions and axioms — Infinite sets and the diagonal method:
Cantor s set theory Explicit logical axioms for mathematics: Frege s
logicism — Russell s paradox discovered — Finitism and formalism:
Hilbert s programme — Decidable predicates and formal theories
The notion of formal proof and first order theory Gddel
numbering — Arithmetization and metamathematics
5. The formal theory N introduced 42
The symbols of the theory — Formation rules — Scope of an operator
Free and bound variables — Substitution The axioms and rules
for N Proof finding made easier Deduction from assumptions
The Deduction Theorem — Introduction and elimination rules
6. Some theorems of N 58
Properties of = — The Replacement Theorem — Properties of+, •, ,
and 0 — Order properties in N Existence and uniqueness of quotient
x CONTENTS
and remainder — The least number principle — Euclid s Theorem —
Equivalents of mathematical induction — Questions about completeness
7. A complete theory for addition 72
Disjunctive normal form — Prenex normal form — The formal theory
D The Reduction Algorithm Completeness and decidability of
D — Properties of congruences — Exercises for Chapter 7
Part II Computability, incompleteness, and undecidability 85
8. Introducing register machines 87
Intuitions about computability The unlimited register ideal
machine described — Drawing flow diagrams — Building from
subprograms — Multiplying the contents of R/ and Ry — The
algorithm for writing programs from flow diagrams — R computability
defined — Church s Thesis
9. Programming computations 99
Examples of R computable functions — Computability of formal
notions v is the godel number of a term A summary outline —
Checking the flow diagram v is the godel number of a formula —
Extrapolation
10. Numeralwise representation 112
Numeralwise expressibility and representability — The numeralwise
representability of R computable functions
11. Incompleteness of the formal theory 119
The incompleteness of N — the unprovability of consistency —
Developments using the diagonal function — R decidability
Tarski s Theorem
12. Undecidable problems 127
The formal theory Q* — The representability of R computable
functions in Q+ — Church s Theorem The halting problem —
Godel numbering programs The universal R machine The
unsolvability of the halting problem
Appendix: answers to exercises 136
Bibliography 187
Index 189
|
| any_adam_object | 1 |
| author | Fisher, Alec |
| author_facet | Fisher, Alec |
| author_role | aut |
| author_sort | Fisher, Alec |
| author_variant | a f af |
| building | Verbundindex |
| bvnumber | BV003665279 |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241 |
| callnumber-search | QA241 |
| callnumber-sort | QA 3241 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)8475061 (DE-599)BVBBV003665279 |
| dewey-full | 512/.72 511.3/076 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 511 - General principles of mathematics |
| dewey-raw | 512/.72 511.3/076 |
| dewey-search | 512/.72 511.3/076 |
| dewey-sort | 3512 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02324nam a2200661 cb4500</leader><controlfield tag="001">BV003665279</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900725s1982 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0198531788</subfield><subfield code="9">0-19-853178-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0198531885</subfield><subfield code="9">0-19-853188-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)8475061</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV003665279</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA241</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.72</subfield><subfield code="2">19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/076</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">03B30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">10N05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fisher, Alec</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Formal number theory and computability</subfield><subfield code="b">A workbook</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Clarendon Press</subfield><subfield code="c">1982</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 190 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Oxford logic guides.</subfield><subfield code="v">7.</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Oxford science publications.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Axiomatique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Calculabilité</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Exercice logique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gödel, Théorème de</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Gödel, Théorème de</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Incomplétude, Théorèmes d'</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Indécidabilité</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nombres, Théorie des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Théorie nombre</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Théorèmes d'incomplétude</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Wiskundige logica</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gödel's theorem</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Incompleteness theorems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Berechenbarkeit</subfield><subfield code="0">(DE-588)4138368-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Berechenbarkeit</subfield><subfield code="0">(DE-588)4138368-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Oxford logic guides.</subfield><subfield code="v">7.</subfield><subfield code="w">(DE-604)BV000013997</subfield><subfield code="9">7.</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002333856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002333856</subfield></datafield></record></collection> |
| id | DE-604.BV003665279 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:03:32Z |
| institution | BVB |
| isbn | 0198531788 0198531885 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002333856 |
| oclc_num | 8475061 |
| open_access_boolean | |
| owner | DE-384 DE-739 DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| owner_facet | DE-384 DE-739 DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | XIII, 190 S. graph. Darst. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford logic guides. |
| series2 | Oxford logic guides. Oxford science publications. |
| spelling | Fisher, Alec Verfasser aut Formal number theory and computability A workbook Oxford Clarendon Press 1982 XIII, 190 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides. 7. Oxford science publications. Axiomatique Calculabilité Exercice logique Gödel, Théorème de Gödel, Théorème de ram Incomplétude, Théorèmes d' ram Indécidabilité Nombres, Théorie des Nombres, Théorie des ram Théorie nombre Théorèmes d'incomplétude Wiskundige logica gtt Gödel's theorem Incompleteness theorems Number theory Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Zahlentheorie (DE-588)4067277-3 s Berechenbarkeit (DE-588)4138368-0 s Oxford logic guides. 7. (DE-604)BV000013997 7. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002333856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fisher, Alec Formal number theory and computability A workbook Oxford logic guides. Axiomatique Calculabilité Exercice logique Gödel, Théorème de Gödel, Théorème de ram Incomplétude, Théorèmes d' ram Indécidabilité Nombres, Théorie des Nombres, Théorie des ram Théorie nombre Théorèmes d'incomplétude Wiskundige logica gtt Gödel's theorem Incompleteness theorems Number theory Berechenbarkeit (DE-588)4138368-0 gnd Mathematische Logik (DE-588)4037951-6 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4138368-0 (DE-588)4037951-6 (DE-588)4067277-3 |
| title | Formal number theory and computability A workbook |
| title_auth | Formal number theory and computability A workbook |
| title_exact_search | Formal number theory and computability A workbook |
| title_full | Formal number theory and computability A workbook |
| title_fullStr | Formal number theory and computability A workbook |
| title_full_unstemmed | Formal number theory and computability A workbook |
| title_short | Formal number theory and computability |
| title_sort | formal number theory and computability a workbook |
| title_sub | A workbook |
| topic | Axiomatique Calculabilité Exercice logique Gödel, Théorème de Gödel, Théorème de ram Incomplétude, Théorèmes d' ram Indécidabilité Nombres, Théorie des Nombres, Théorie des ram Théorie nombre Théorèmes d'incomplétude Wiskundige logica gtt Gödel's theorem Incompleteness theorems Number theory Berechenbarkeit (DE-588)4138368-0 gnd Mathematische Logik (DE-588)4037951-6 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Axiomatique Calculabilité Exercice logique Gödel, Théorème de Incomplétude, Théorèmes d' Indécidabilité Nombres, Théorie des Théorie nombre Théorèmes d'incomplétude Wiskundige logica Gödel's theorem Incompleteness theorems Number theory Berechenbarkeit Mathematische Logik Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002333856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000013997 |
| work_keys_str_mv | AT fisheralec formalnumbertheoryandcomputabilityaworkbook |