Ordinal computability: an introduction to infinitary machines
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2019]
|
| Series: | De Gruyter series in logic and its applications
volume 9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | VIII, 333 Seiten Illustrationen 25 cm, 719 g |
| ISBN: | 9783110495621 3110495627 |
Staff View
MARC
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| 100 | 1 | |a Carl, Merlin |d 1982- |e Verfasser |0 (DE-588)1140438417 |4 aut | |
| 245 | 1 | 0 | |a Ordinal computability |b an introduction to infinitary machines |c Merlin Carl |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 300 | |a VIII, 333 Seiten |b Illustrationen |c 25 cm, 719 g | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a De Gruyter series in logic and its applications |v volume 9 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1
1.1
1.2
1.3
1.4
INTRODUCTION
*
1
ABOUT
THIS
BOOK
-----
1
WHAT
HAPPENED
SO
FAR?
*
2
SUMMARY
-----
4
ACKNOWLEDGMENTS
*
6
2
2.1
2.1.1
2.1.2
2.2
2.2.1
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.4
2.5
2.5.1
2.5.2
2.5.3
2.5.4
2.5.5
2.5.6
2.5.7
2.6
2.7
2.7.1
2.7.2
2.7.3
2.8
MACHINE
MODELS
OF
TRANSFINITE
COMPUTABILITY
*
9
INTRODUCTION
*
9
SIMULATION
OF
MACHINE
MODELS
*
11
HALTING
PROBLEMS
*
13
INFINITARY
ANALOGUES
OF
REGISTER
MACHINES
*
13
WITRM-COMPUTATIONS
-----
18
INFINITE
TIME
CR-REGISTER
MACHINES
*
20
ITRMS
WITH
ONE
REGISTER
-----
25
CODING
TRANSITIVE
^-STRUCTURES
*
30
TESTING
WELL-FOUNDEDNESS
*
31
EVALUATING
TRUTH
PREDICATES
AND
OTHER
PROPERTIES
OF
STRUCTURES
*
38
ORDINAL
REGISTER
MACHINES
*
42
INFINITARY
ANALOGUES
OF
TURING
MACHINES
*
44
INFINITE
TIME
TURING
MACHINES
*
45
STACK
REPRESENTATION
FOR
TAPE
MODELS
*
48
COMPUTABILITY
NOTIONS
FOR
TAPE
MODELS
*
49
CLOCKABLE
ORDINALS
*
56
CR-ITTMS
AND
CR-ITRMS
-----
61
WEAK
ITTMS-----
62
ORDINAL
TURING
MACHINES
*
66
ABSOLUTENESS
OF
COMPUTATIONS
*
67
BEYOND
COMPUTABILITY:
THE
JUMP
OPERATOR
*
68
FURTHER
MODELS
-----
69
DETERMINISTIC
ORDINAL
AUTOMATA
*
69
INFINITE
TIME
BLUM-SHUB-SMALE
MACHINES
*
71
FURTHER
MODELS
*
73
EXERCISES
*
74
3
3.1
3.1.1
3.1.2
3.1.3
COMPUTABILITY
STRENGTH
*
77
PRELIMINARIES
*
77
HIERARCHIES
OF
SETS
AND
FORMULAS
*
77
BASICS
ON
THE
CONSTRUCTIVE
HIERARCHY
*
79
ADMISSIBILITY
-----83
VI
*
CONTENTS
3.1.4
3.1.5
3.2
ADMISSIBILITY
OF
CONSTRUCTIBLE
LEVELS
*
88
COMPUTATIONS
AND
THE
CONSTRUCTIBLE
HIERARCHY
*
92
THE
COMPUTABILITY
STRENGTH
OF
ORDINAL
REGISTER
MACHINES
AND
CR-REGISTER
MACHINES
*
92
3.2.1
3.2.2
3.3
3.4
3.4.1
3.5
3.6
3.6.1
3.6.2
3.6.3
3.6.4
3.6.5
3.6.6
3.7
3.7.1
3.7.2
3.8
3.9
LOWER
BOUNDS
FOR
ORMS
*
94
ORMS
WITHOUT
PARAMETERS
*
101
THE
COMPUTATIONAL
STRENGTH
OF
CR-REGISTER
MACHINES
*
102
CR-WLTRMS
AND
CR-ITRMS
*
105
LOWER
BOUNDS
*
114
CR-TMS
AND
OTMS
*
118
CR-ITTMS
AND
THE
Z
2
-MACHINE
*
120
UPPER
BOUNDS
*
125
THE
I
2
MACHINE
*
128
A-ITTM-COMPUTABILITY
AND
THE
THEORY
MACHINE
*
130
FURTHER
CONSEQUENCES
*
142
FURTHER
RESULTS
ON
O-ITTMS
*
145
WITHOUT
PARAMETERS
*
146
ACCIDENTAL
AND
EVENTUAL
WRITABILITY
*
148
ACCIDENTAL
AND
EVENTUAL
WRITABILITY
FOR
ITRMS
*
148
ACCIDENTAL
AND
EVENTUAL
WRITABILITY
FOR
OTMS
*
149
SUMMARY
*
152
EXERCISES
*
153
4
4.1
4.1.1
4.2
4.2.1
4.2.2
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.4
4.4.1
4.5
4.6
4.7
RECOGNIZABILITY
*
157
PRELIMINARIES
*
157
EXTENDED
TRUTH
PREDICATES
*
158
LOST
MELODIES
*
159
A-MACHINES
*
165
WEAK
ITRMS-----
165
RECOGNIZABILITY
FOR
INFINITE
TIME
REGISTER
MACHINES
*
172
GAPS
*
173
ARISTOPHANEAN
PAIRS
*
176
RECOGNIZABILITY
OF
THE
HALTING
NUMBERS
*
178
A
MACHINE-FREE
CHARACTERIZATION
OF
ITRM-RECOGNIZABILITY
*
180
RECOGNIZABILITY
FOR
ORDINAL
TURING
MACHINES
*
181
THE
RECOGNIZABLE
CLOSURE
FOR
OTMS
*
185
VARIANTS
OF
RECOGNIZABILITY
*
190
SUMMARY
*
192
EXERCISES
*
193
5
5.1
RANDOMNESS
*
195
INTRODUCTION
*
195
CONTENTS
*
VII
5.2
5.3
5.3.1
5.3.2
5.3.3
5.4
5.5
5.6
5.7
5.7.1
PRELIMINARIES
ON
FORCING
AND
SETS
OF
REAL
NUMBERS
*
195
INFINITARY
ANALOGUES
OF
SACK
*
S
THEOREM
*
203
SACKS
*
THEOREM
FOR
WITRMS
AND
ITRMS
*
204
SACKS
*
THEOREM
FOR
ITTMS
-----
205
ANALOGUES
FOR
OTMS
-----
207
RANDOMNESS
AND
RECOGNIZABILITY
*
210
SOME
RESULTS
ON
ITRM-GENERICITY
*
212
OTMS
AND
GENERICITY
*
216
FURTHER
RESULTS
*
216
ITTMS
AND
RANDOMNESS
*
217
6
6.1
6.2
6.2.1
6.3
6.4
6.4.1
6.5
6.6
DEGREE
THEORY
*
219
PRELIMINARIES
*
219
DEGREE
THEORY
FOR
ITTMS
*
219
EVENTUALLY
WRITABLE
DEGREES
*
224
DEGREE
THEORY
FOR
OTMS
AND
ORMS
*
225
DEGREE
THEORY
FOR
ITRMS
*
230
DEGREES
OF
RECOGNIZABLES
*
233
SOME
RESULTS
ON
THE
DEGREE
THEORY
OF
OTHER
MODELS
*
236
DEGREES
OF
RECOGNIZABILITY
*
236
7
7.1
7.2
7.2.1
7.2.2
7.3
7.3.1
7.3.2
7.3.3
COMPLEXITY
*
239
INTRODUCTION
*
239
COMPLEXITY
THEORY
FOR
ITTMS
-----
241
ITTM-COMPLEXITY
WITH
DEPENDENCY
ON
THE
INPUT
*
244
SPACE
COMPLEXITY
FOR
ITTMS
*
245
COMPLEXITY
THEORY
FOR
OTMS
*
247
NP-COMPLETENESS
FOR
OTMS
*
248
STRUCTURAL
PROPERTIES
OF
NP
*
252
STRONG
SPACE
BOUNDS
AND
REGULARITY
*
256
8
8.1
8.2
8.3
8.4
8.4.1
8.5
8.6
8.6.1
8.7
APPLICATIONS
AND
INTERACTIONS
*
257
INTRODUCTION
*
257
ORDINAL
TURING
MACHINES
AND
THE
CONSTRUCTIVE
HIERARCHY
*
257
INFINITARY
COMPUTATIONS
AND
DESCRIPTIVE
SET
THEORY
*
258
INFINITE
TIME
COMPUTABILITY
AND
BOREL
REDUCIBILITY
*
261
ITTM-REDUCIBILITY
AND
BOREL
REDUCIBILITY
*
262
INFINITE
TIME
COMPUTABLE
MODEL
THEORY
*
264
GENERALIZED
EFFECTIVE
REDUCIBILITY
*
265
AN
APPLICATION:
VERSIONS
OF
THE
AXIOM
OF
CHOICE
*
272
FURTHER
PROSPECTS
*
275
VIII
*
CONTENTS
9
PHILOSOPHICAL
ASPECTS
*
277
9.1
INFINITARY
CONSTRUCTIONS
IN
MATHEMATICS
*
277
9.2
IDEALIZED
AGENTS
IN
THE
PHILOSOPHY
OF
MATHEMATICS
*
281
9.2.1
IDEALIZED
AGENTS
IN
G.
TAKEUTI
*
S
FOUNDATIONAL
POSITION
*
282
9.2.2
IDEALIZED
AGENTS
AND
PHILIPP
KITCHER
*
S
MATHEMATICAL
EMPIRICISM
*
283
9.2.3
IDEALIZED
AGENTS
IN
RAMSEY
*
S
FOUNDATIONS
OF
MATHEMATICS
*
283
9.2.4
REMARKS
-----
284
9.3
INFINITARY
MACHINES
AS
FORMAL
MODELS
FOR
IDEALIZED
AGENTS
*
285
9.3.1
THE
IDEALIZED
AGENT
OF
SET
THEORY
*
286
9.3.2
TRANSFINITE
WORKING
TIME
*
287
9.3.3
ELEMENTARY
STEPS
*
289
9.3.4
IDEALIZED
AGENT
MACHINES
AND
ORDINAL
TURING
MACHINES
*
290
9.3.5
CRITERIA
FOR
A
DEFENSIBLE
CHURCH-TURING
THESIS
FOR
THE
TRANSFINITE
*
291
9.4
INFINITARY
AGENCY
AS
MODELED
BY
OTMS
*
295
9.4.1
TRANSFINITE
CREATIVE
SUBJECTS?
*
299
9.5
INFINITE
TIME
TURING
MACHINES
AND
THE
REVISION
THEORY
OF
TRUTH
*
302
9.5.1
THE
REVISION
THEORY
OF
TRUTH
*
303
9.5.2
CONNECTING
REVISION
THEORY
OF
TRUTH
AND
ITTMS
*
308
9.5.3
APPLYING
THE
CONNECTION
*
309
BIBLIOGRAPHY-----
313
INDEX
*
323
|
| any_adam_object | 1 |
| author | Carl, Merlin 1982- |
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| discipline | Informatik Mathematik |
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| id | DE-604.BV046272833 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:40:12Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110495621 3110495627 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031650607 |
| oclc_num | 1136470238 |
| open_access_boolean | |
| owner | DE-634 DE-703 DE-11 DE-384 |
| owner_facet | DE-634 DE-703 DE-11 DE-384 |
| physical | VIII, 333 Seiten Illustrationen 25 cm, 719 g |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter series in logic and its applications |
| series2 | De Gruyter series in logic and its applications |
| spelling | Carl, Merlin 1982- Verfasser (DE-588)1140438417 aut Ordinal computability an introduction to infinitary machines Merlin Carl Berlin ; Boston De Gruyter [2019] VIII, 333 Seiten Illustrationen 25 cm, 719 g txt rdacontent n rdamedia nc rdacarrier De Gruyter series in logic and its applications volume 9 Registermaschine (DE-588)4177439-5 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Turing-Maschine (DE-588)4203525-9 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 s Turing-Maschine (DE-588)4203525-9 s Registermaschine (DE-588)4177439-5 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-049615-4 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-049291-0 De Gruyter series in logic and its applications volume 9 (DE-604)BV012743398 9 B:DE-101 application/pdf https://d-nb.info/1175756814/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031650607&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carl, Merlin 1982- Ordinal computability an introduction to infinitary machines De Gruyter series in logic and its applications Registermaschine (DE-588)4177439-5 gnd Berechenbarkeit (DE-588)4138368-0 gnd Turing-Maschine (DE-588)4203525-9 gnd |
| subject_GND | (DE-588)4177439-5 (DE-588)4138368-0 (DE-588)4203525-9 |
| title | Ordinal computability an introduction to infinitary machines |
| title_auth | Ordinal computability an introduction to infinitary machines |
| title_exact_search | Ordinal computability an introduction to infinitary machines |
| title_full | Ordinal computability an introduction to infinitary machines Merlin Carl |
| title_fullStr | Ordinal computability an introduction to infinitary machines Merlin Carl |
| title_full_unstemmed | Ordinal computability an introduction to infinitary machines Merlin Carl |
| title_short | Ordinal computability |
| title_sort | ordinal computability an introduction to infinitary machines |
| title_sub | an introduction to infinitary machines |
| topic | Registermaschine (DE-588)4177439-5 gnd Berechenbarkeit (DE-588)4138368-0 gnd Turing-Maschine (DE-588)4203525-9 gnd |
| topic_facet | Registermaschine Berechenbarkeit Turing-Maschine |
| url | https://d-nb.info/1175756814/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031650607&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012743398 |
| work_keys_str_mv | AT carlmerlin ordinalcomputabilityanintroductiontoinfinitarymachines AT walterdegruytergmbhcokg ordinalcomputabilityanintroductiontoinfinitarymachines |
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