Class information for:
Level 1: HILBERTS TENTH PROBLEM//DIOPHANTINE DEFINITION//BUCHIS PROBLEM

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
25185 288 17.4 28%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
205 3       MATHEMATICS//JOURNAL OF NUMBER THEORY//ACTA ARITHMETICA 52461
376 2             JOURNAL OF NUMBER THEORY//MATHEMATICS//ACTA ARITHMETICA 17147
25185 1                   HILBERTS TENTH PROBLEM//DIOPHANTINE DEFINITION//BUCHIS PROBLEM 288

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 HILBERTS TENTH PROBLEM authKW 1933091 10% 65% 28
2 DIOPHANTINE DEFINITION authKW 742176 2% 100% 7
3 BUCHIS PROBLEM authKW 477110 2% 75% 6
4 BUCHI SEQUENCES authKW 318076 1% 100% 3
5 FM REPRESENTABILITY authKW 318076 1% 100% 3
6 PASCALS TRIANGLE MODULE N authKW 318076 1% 100% 3
7 FINITE ARITHMETIC authKW 238555 1% 75% 3
8 HILBERTS 10TH PROBLEM authKW 238555 1% 75% 3
9 BUCHI PROBLEM authKW 212050 1% 100% 2
10 DIOPHANTINE UNDECIDABILITY authKW 212050 1% 100% 2

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Logic 24209 20% 0% 58
2 Mathematics 11799 86% 0% 248
3 Mathematics, Applied 898 23% 0% 66
4 Computer Science, Theory & Methods 38 4% 0% 11
5 Computer Science, Software Engineering 28 3% 0% 8
6 Philosophy 26 2% 0% 5
7 Operations Research & Management Science 9 2% 0% 5
8 Multidisciplinary Sciences 6 1% 0% 3
9 History & Philosophy of Science 1 0% 0% 1
10 Computer Science, Artificial Intelligence 0 1% 0% 2

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 VAKGRP KWANTITAT TECH 212050 1% 100% 2
2 EQUIPE LOG URA 753 106025 0% 100% 1
3 KRAKOW PRZEDMIESCIE 3 106025 0% 100% 1
4 LLAIC 1 106025 0% 100% 1
5 LOG ALGORITHM INFORMAT CLERMONT 1 106025 0% 100% 1
6 LOG ALGORITHM INFORMAT DE CLERMONT 1 106025 0% 100% 1
7 WISKUNDE STAT ACTUARIAAT 106025 0% 100% 1
8 EA 4213 26505 0% 25% 1
9 LOGIC 26505 0% 25% 1
10 MECAN MATH 26505 0% 25% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 JOURNAL OF SYMBOLIC LOGIC 42299 12% 1% 34
2 ANNALS OF PURE AND APPLIED LOGIC 6209 4% 1% 11
3 JOURNAL OF NUMBER THEORY 4406 5% 0% 14
4 COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 3188 6% 0% 16
5 ACTA ARITHMETICA 2657 3% 0% 9
6 JOURNAL OF ALGEBRA 2620 6% 0% 18
7 REPORTS ON MATHEMATICAL LOGIC 2354 0% 2% 1
8 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 2264 7% 0% 19
9 MATHEMATICAL LOGIC QUARTERLY 2246 2% 0% 5
10 ZEITSCHRIFT FUR MATHEMATISCHE LOGIK UND GRUNDLAGEN DER MATHEMATIK 1922 1% 1% 3

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 HILBERTS TENTH PROBLEM 1933091 10% 65% 28 Search HILBERTS+TENTH+PROBLEM Search HILBERTS+TENTH+PROBLEM
2 DIOPHANTINE DEFINITION 742176 2% 100% 7 Search DIOPHANTINE+DEFINITION Search DIOPHANTINE+DEFINITION
3 BUCHIS PROBLEM 477110 2% 75% 6 Search BUCHIS+PROBLEM Search BUCHIS+PROBLEM
4 BUCHI SEQUENCES 318076 1% 100% 3 Search BUCHI+SEQUENCES Search BUCHI+SEQUENCES
5 FM REPRESENTABILITY 318076 1% 100% 3 Search FM+REPRESENTABILITY Search FM+REPRESENTABILITY
6 PASCALS TRIANGLE MODULE N 318076 1% 100% 3 Search PASCALS+TRIANGLE+MODULE+N Search PASCALS+TRIANGLE+MODULE+N
7 FINITE ARITHMETIC 238555 1% 75% 3 Search FINITE+ARITHMETIC Search FINITE+ARITHMETIC
8 HILBERTS 10TH PROBLEM 238555 1% 75% 3 Search HILBERTS+10TH+PROBLEM Search HILBERTS+10TH+PROBLEM
9 BUCHI PROBLEM 212050 1% 100% 2 Search BUCHI+PROBLEM Search BUCHI+PROBLEM
10 DIOPHANTINE UNDECIDABILITY 212050 1% 100% 2 Search DIOPHANTINE+UNDECIDABILITY Search DIOPHANTINE+UNDECIDABILITY

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 MORET-BAILLY, L , SHLAPENTOKH, A , (2009) DIOPHANTINE UNDECIDABILITY OF HOLOMORPHY RINGS OF FUNCTION FIELDS OF CHARACTERISTIC 0.ANNALES DE L INSTITUT FOURIER. VOL. 59. ISSUE 5. P. 2103-2118 31 100% 1
2 SHLAPENTOKH, A , (2005) FIRST-ORDER DEFINITIONS OF RATIONAL FUNCTIONS AND S-INTEGERS OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTIONS OF CHARACTERISTIC 0.ANNALS OF PURE AND APPLIED LOGIC. VOL. 136. ISSUE 3. P. 267-283 25 100% 2
3 SHLAPENTOKH, A , (2012) ELLIPTIC CURVE POINTS AND DIOPHANTINE MODELS OF Z IN LARGE SUBRINGS OF NUMBER FIELDS.INTERNATIONAL JOURNAL OF NUMBER THEORY. VOL. 8. ISSUE 6. P. 1335-1365 20 95% 0
4 EISENTAGER, K , (2013) THE WORK OF KIM AND ROUSH ON QUESTIONS OF DECIDABILITY IN ALGEBRA AND NUMBER THEORY.ACTA APPLICANDAE MATHEMATICAE. VOL. 126. ISSUE 1. P. 29-33 18 100% 1
5 SHLAPENTOKH, A , (2002) ON DIOPHANTINE DEFINABILITY AND DECIDABILITY IN SOME RINGS OF ALGEBRAIC FUNCTIONS OF CHARACTERISTIC 0.JOURNAL OF SYMBOLIC LOGIC. VOL. 67. ISSUE 2. P. 759 -786 20 100% 3
6 SHLAPENTOKH, A , (2000) HILBERT'S TENTH PROBLEM FOR ALGEBRAIC FUNCTION FIELDS OVER INFINITE FIELDS OF CONSTANTS OF POSITIVE CHARACTERISTIC.PACIFIC JOURNAL OF MATHEMATICS. VOL. 193. ISSUE 2. P. 463-500 20 100% 10
7 SHLAPENTOKH, A , (2007) DIOPHANTINE DEFINABILITY AND DECIDABILITY IN EXTENSIONS OF DEGREE 2 OF TOTALLY REAL FIELDS.JOURNAL OF ALGEBRA. VOL. 313. ISSUE 2. P. 846-896 16 100% 1
8 SHLAPENTOKH, A , (2009) RINGS OF ALGEBRAIC NUMBERS IN INFINITE EXTENSIONS OF Q AND ELLIPTIC CURVES RETAINING THEIR RANK.ARCHIVE FOR MATHEMATICAL LOGIC. VOL. 48. ISSUE 1. P. 77 -114 16 94% 1
9 EISENTRAGER, K , SHLAPENTOKH, A , (2009) UNDECIDABILITY IN FUNCTION FIELDS OF POSITIVE CHARACTERISTIC.INTERNATIONAL MATHEMATICS RESEARCH NOTICES. VOL. . ISSUE 21. P. 4051 -4086 14 100% 4
10 SHLAPENTOKH, A , (2002) DEFINING INTEGRALITY AT PRIME SETS OF HIGH DENSITY OVER FUNCTION FIELDS.MONATSHEFTE FUR MATHEMATIK. VOL. 135. ISSUE 1. P. 59 -67 17 100% 1

Classes with closest relation at Level 1


Rank Class id link
1 18628 ABSOLUTE GALOIS GROUP//HILBERTIAN FIELDS//DEFINABLE VALUATIONS
2 29968 SCATTERED SUBWORD//PARIKH MATRIX//SUBWORD
3 4357 ARITHMETIC DYNAMICS//ANDRE OORT CONJECTURE//ACTA ARITHMETICA
4 19216 MEROMORPHIC MAPPING//SECOND MAIN THEOREM//TRUNCATED MULTIPLICITY
5 19168 SHIFT OF FINITE TYPE//ZD//SOFIC
6 14361 BOUNDED ARITHMETIC//PROOF COMPLEXITY//PROPOSITIONAL PROOF COMPLEXITY
7 28799 AXIOM OF CHOICE//WEAK AXIOMS OF CHOICE//BOOLEAN PRIME IDEAL THEOREM
8 11070 ELLIPTIC CURVES//MODULAR CURVES//CONGRUENT NUMBERS
9 13494 FINITE MODEL THEORY//DESCRIPTIVE COMPLEXITY//CONSTRAINT DATABASES
10 9563 O MINIMALITY//O MINIMAL STRUCTURES//O MINIMAL

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