WebIndex < Mizar

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03B General logic Section P S 03B05 Classical propositional logic 03B10 Classical first order logic 9 03B15 Higher order ...

03B10

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General logic Classical first order logic Primary classification # Article 1 qc lang1 A First Order Language Piotr Rudnicki and Andrzej Trybulec 2 qc ...

03C

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03C Model theory Section P S 03C05 Equational classes, universal algebra See also 08Axx, 08Bxx, 18C05 03C07 Basic properties of first ...

03C62

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Model theory Models of arithmetic and set theory Primary classification # Article 1 zf lang A Model of ZF Set Theory Language Grzegorz Bancerek 2 zf ...

03E

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03E Set theory Section P S 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other ...

03E10

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03E10 Set theory Ordinal and cardinal numbers Primary classification # Article 1 ordinal1 The Ordinal Numbers. Transfinite Induction and Defining by Transfinite ...

03E20

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03E20 Set theory Other classical set theory Primary classification # Article 1 hidden Built in Concepts Andrzej Trybulec 2 tarski Tarski Grothendieck ...

03E25

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03E25 Set theory Axiom of choice and related propositions Primary classification # Article Secondary classification # Article ...

03E55

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03E55 Set theory Large cardinals Primary classification # Article 1 card fil Basic facts about inaccessible and measurable cardinals Josef Urban 2 card ...

03E65

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03E65 Set theory Other hypotheses and axioms Primary classification # Article Secondary classification # Article 1 tarski Tarski ...

03E99

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03E99 Set theory None of the above, but in this section Primary classification # Article 1 finseq 1 Segments of Natural Numbers and Finite Sequences Grzegorz ...

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05 Combinatorics Section P S 05A Enumerative combinatorics 05B Designs and configurations For applications of design theory, see 94C30 ...

05C

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05C Graph theory Section P S 05C05 Trees 6 05C07 Degree sequences 05C10 Topological graph theory, imbedding See also 57M15 ...

05C05

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05C05 Graph theory Trees Primary classification # Article 1 trees 1 Introduction to Trees Grzegorz Bancerek 2 trees 2 K\"onig's Lemma Grzegorz Bancerek ...

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06 Order, lattices, ordered algebraic structures Section P S 06A Ordered sets 06B Lattices See also 03G10 2 06C Modular lattices ...

06B

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06B Lattices Section P S 06B05 Structure theory 06B10 Ideals, congruence relations 06B15 Representation theory ...

06B99

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06B99 Lattices None of the above, but in this section Primary classification # Article 1 nat lat The Lattice of Natural Numbers and The Sublattice of it ...

06E

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06E Boolean algebras (Boolean rings) Section P S 06E05 Structure theory 06E10 Chain conditions, complete algebras 06E15 ...

06E30

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06E30 Boolean algebras (Boolean rings) Boolean functions Primary classification # Article 1 xboolean On the Arithmetic of Boolean Values Library Committee ...

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11 Number theory Section P S 11A Elementary number theory For analogues in number fields, see 11R04 11 11B Sequences and sets ...

11A

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11A Elementary number theory Section P S 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors 5 11A07 Congruences ...

11A05

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11A05 Elementary number theory Multiplicative structure; Euclidean algorithm; greatest common divisors Primary classification # Article 1 nat 1 The Fundamental ...

11A25

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11A25 Elementary number theory Arithmetic functions; related numbers; inversion formulas Primary classification # Article 1 euler 1 Euler's Function Yoshinori ...

11A41

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11A41 Elementary number theory Primes Primary classification # Article 1 nat 3 Fundamental {T}heorem of {A}rithmetic Artur Korni{\l}owicz and Piotr Rudnicki ...

11A51

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11A51 Elementary number theory Factorization; primality Primary classification # Article 1 pepin Public Key Cryptography and Pepin's Test for the Primality ...

11A55

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11A55 Elementary number theory Continued fractions Primary classification # Article 1 real 3 Simple Continued Fractions and Their Convergents Bo Li , ...

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12 Field theory and polynomials Section P S 12D Real and complex fields 6 12E General field theory 12F Field extensions ...

12D

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12D Real and complex fields Section P S 12D05 Polynomials: factorization 12D10 Polynomials: location of zeros (algebraic theorems ...

12D99

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Real and complex fields None of the above, but in this section Primary classification # Article 1 numbers Subsets of Complex Numbers Andrzej Trybulec ...

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13 Commutative rings and algebras Section P S 13A General commutative ring theory 13B Ring extensions and related topics ...

13F

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13F Arithmetic rings and other special rings Section P S 13F05 Dedekind, Prüfer and Krull rings and their generalizations 13F07 Euclidean ...

13F07

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13F07 Arithmetic rings and other special rings Euclidean rings and generalizations Primary classification # Article 1 int 3 The Ring of Integers, Euclidean ...

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15 Linear and multilinear algebra; matrix theory Section P S 15A03 Vector spaces, linear dependence, rank 16 1 15A04 Linear transformations ...

15A03

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15A03 Linear and multilinear algebra; matrix theory Vector spaces, linear dependence, rank Primary classification # Article 1 rlvect 1 Vectors in Real ...

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16 Associative rings and algebras Section P S 16B General and miscellaneous 16D Modules, bimodules and ideals 13 16E ...

16D

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16D Modules, bimodules and ideals Section P S 16D10 General module theory 11 16D20 Bimodules 16D25 Ideals ...

16D10

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16D10 Modules, bimodules and ideals General module theory Primary classification # Article 1 vectsp 2 Construction of Rings and Left , Right , and Bi Modules ...

16D40

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16D40 Modules, bimodules and ideals Free, projective, and flat modules and ideals Primary classification # Article 1 mod 3 Free Modules Michal Muzalewski ...

16D90

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16D90 Modules, bimodules and ideals Module categories Primary classification # Article 1 modcat 1 Category of Left Modules Micha{\l} Muzalewski ...

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18 Category theory; homological algebra Section P S 18A General theory of categories and functors 8 18B Special categories 1 ...

18A

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18A General theory of categories and functors Section P S 18A05 Definitions, generalizations 8 18A10 Graphs, diagram schemes, precategories ...

18A05

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18A05 General theory of categories and functors Definitions, generalizations Primary classification # Article 1 cat 1 Introduction to Categories and Functors ...

18B

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18B Special categories Section P S 18B05 Category of sets, characterizations See also 03 xx 18B10 Category of relations, additive relations ...

18B40

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18B40 Special categories Groupoids, semigroupoids, semigroups, groups Primary classification # Article 1 grcat 1 Categories of Groups Michal Muzalewski ...

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20 Group theory and generalizations Section P S 20A Foundations 6 20B Permutation groups 20C Representation theory of ...

20A

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20A Foundations Section P S 20A05 Axiomatics and elementary properties 6 20A10 Metamathematical considerations For word problems, see ...

20A05

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20A05 Foundations Axiomatics and elementary properties Primary classification # Article 1 group 1 Groups Wojciech A. Trybulec 2 group 2 Subgroup and ...

20E

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20E Structure and classification of infinite or finite groups Section P S 20E05 Free nonabelian groups 20E06 Free products, free products ...

20E15

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20E15 Structure and classification of infinite or finite groups Chains and lattices of subgroups, subnormal subgroups Primary classification # Article 1 ...

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26 Real functions Section P S 26A Functions of one variable 29 26B Functions of several variables 26C Polynomials, rational ...

26A

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26A Functions of one variable Section P S 26A03 Foundations: limits and generalizations, elementary topology of the line 6 26A06 One variable ...

26A03

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26A03 Functions of one variable Foundations: limits and generalizations, elementary topology of the line Primary classification # Article 1 arytm 2 Non ...

26A09

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26A09 Functions of one variable Elementary functions Primary classification # Article 1 square 1 Some Properties of Real Numbers. Operations: min, max, ...

26A24

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26A24 Functions of one variable Differentiation (functions of one variable): general theory, generalized derivatives, meanvalue theorems Primary classification ...

26A99

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26A99 Functions of one variable None of the above, but in this section Primary classification # Article 1 arytm 3 Arithmetic of Non Negative Rational Numbers ...

26D

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26D Inequalities Section P S 26D05 Inequalities for trigonometric functions and polynomials 26D07 Inequalities involving other types ...

26D15

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26D15 Inequalities Inequalities for sums, series and integrals Primary classification # Article 1 series 3 On the Partial Product of Series and Related ...

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28 Measure and integration Section P S 28A Classical measure theory 13 28B Set functions, measures and integrals with values in abstract ...

28A

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28A Classical measure theory Section P S 28A05 Classes of sets (Borel fields, $\sigma$ rings, etc.), measurable sets, Suslin sets, analytic sets ...

28A12

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28A12 Classical measure theory Contents, measures, outer measures, capacities Primary classification # Article 1 measure1 The $\sigma$ additive Measure ...

28A20

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28A20 Classical measure theory Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence Primary classification # Article ...

28A25

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28A25 Classical measure theory Integration with respect to measures and other set functions Primary classification # Article 1 mesfunc3 Lebesgue Integral ...

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33 Special functions Section P S 33B Elementary classical functions 8 33C Hypergeometric functions 33D Basic hypergeometric ...

33B

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33B Elementary classical functions Section P S 33B10 Exponential and trigonometric functions 8 33B15 Gamma, beta and polygamma functions ...

33B10

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33B10 Elementary classical functions Exponential and trigonometric functions Primary classification # Article 1 sin cos Trigonometric Functions and Existence ...

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40 Sequences, series, summability Section P S 40A Convergence and divergence of infinite limiting processes 6 40B05 Multiple sequences ...

40A

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40A Convergence and divergence of infinite limiting processes Section P S 40A05 Convergence and divergence of series and sequences 6 40A10 ...

40A05

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40A05 Convergence and divergence of infinite limiting processes Convergence and divergence of series and sequences Primary classification # Article 1 seq ...

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46 Functional analysis Section P S 46A Topological linear spaces and related structures For function spaces, see 46E 46B Normed linear ...

46C

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46C Inner product spaces and their generalizations, Hilbert spaces Section P S 46C05 Hilbert and pre Hilbert spaces: geometry and topology (including ...

46C05

AdamGrabowski

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Inner product spaces and their generalizations, Hilbert spaces Primary classification # Article 1 bhsp 1 Introduction to Banach and Hilbert Spaces Part ...

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54 General topology Section P S 54A Generalities 54B Basic constructions 54C Maps and general types of spaces defined ...

54E

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54E Spaces with richer structures Section P S 54E05 Proximity structures and generalizations 54E15 Uniform structures and generalizations ...

54E35

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54E35 Spaces with richer structures Metric spaces, metrizability Primary classification # Article 1 metric 1 Metric Spaces Stanis{\l}awa Kanas, Adam Lecko ...

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68 Computer science Section P S 68M Computer system organization 68N Software 1 68P Theory of data 4 68Q Theory ...

68N

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68N Software Section P S 68N01 General 68N15 Programming languages 68N17 Logic programming 68N18 Functional ...

68N20

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68N20 Software Compilers and interpreters Primary classification # Article 1 scm comp A compiler of arithmetic expressions for { \bf SCM } Grzegorz Bancerek ...

68P

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68P Theory of data Section P S 68P01 General 68P05 Data structures 68P10 Searching and sorting 4 68P15 Database ...

68P10

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68P10 Theory of data Searching and sorting Primary classification # Article scmbsort Bubble Sort on SCM FSA JingChao Chen and Yatsuka Nakamura scmisort ...

68Q

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68Q Theory of computing Section P S 68Q01 General 68Q05 Models of computation (Turing machines, etc.) See also 03D10, 81P68 38 ...

68Q05

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68Q05 Theory of computing Models of computation (Turing machines, etc.) Primary classification # Article 1 ami 1 A Mathematical Model of CPU Yatsuka Nakamura ...

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94 Information and communication, circuits Section P S 94A Communication, information 94B Theory of error correcting codes and error ...

94C

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94C Circuits, networks Section P S 94C05 Analytic circuit theory 94C10 Switching theory, application of Boolean algebra; Boolean functions ...

94C99