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1 | (34) |
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1 | (13) |
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1.1.1 The Search for Functorial Solutions to Certain Representation Problems |
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2 | (3) |
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1.1.2 Partially Functorial Solutions to Representation Problems |
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5 | (3) |
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1.1.3 Contents of the Book |
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8 | (4) |
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1.1.4 How Not to Read the Book |
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12 | (2) |
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14 | (10) |
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14 | (1) |
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1.2.2 Stone Duality for Boolean Algebras |
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15 | (1) |
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1.2.3 Partially Ordered Sets (Posets) and Lattices |
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15 | (2) |
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17 | (3) |
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1.2.5 Directed Colimits of First-Order Structures |
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20 | (4) |
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1.3 Kappa-Presented and Weakly Kappa-Presented Objects |
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24 | (2) |
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1.4 Extension of a Functor by Directed Colimits |
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26 | (7) |
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1.5 Projectability Witnesses |
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33 | (2) |
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2 Boolean Algebras That Are Scaled with Respect to a Poset |
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35 | (16) |
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2.1 Pseudo Join-Semilattices, Supported Posets, and Almost Join-Semilattices |
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35 | (3) |
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2.2 P-Normed Spaces, P-Scaled Boolean Algebras |
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38 | (3) |
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2.3 Directed Colimits and Finite Products of P-Scaled Boolean Algebras |
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41 | (2) |
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2.4 Finitely Presented P-Scaled Boolean Algebras |
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43 | (2) |
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2.5 Normal Morphisms in BoolP and in BTopP |
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45 | (2) |
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2.6 Norm-Coverings of a Poset; The Structures 2[ p] and F(X) |
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47 | (4) |
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3 The Condensate Lifting Lemma (CLL) |
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51 | (30) |
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3.1 The Functor A → A S; Condensates |
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51 | (2) |
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3.2 Lifters and the Armature Lemma |
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53 | (4) |
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3.3 The Lowenheim-Skolem Condition and the Buttress Lemma |
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57 | (3) |
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3.4 Larders and the Condensate Lifting Lemma |
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60 | (3) |
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3.5 Infinite Combinatorics and Lambda-Lifters |
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63 | (7) |
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3.6 Lifters, Retracts, and Pseudo-Retracts |
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70 | (4) |
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3.7 Lifting Diagrams Without Assuming Lifters |
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74 | (3) |
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3.8 Left and Right Larders |
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77 | (4) |
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4 Getting Larders from Congruence Lattices of First-Order Structures |
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81 | (36) |
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4.1 The Category of All Monotone-Indexed Structures |
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82 | (4) |
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4.2 Directed Colimits of Monotone-Indexed Structures |
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86 | (3) |
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4.3 The Relative Congruence Lattice Functor with Respect to a Generalized Quasivariety |
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89 | (5) |
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4.4 Preservation of Small Directed Colimits by the Relative Compact Congruence Functor |
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94 | (1) |
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4.5 Ideal-Induced Morphisms and Projectability Witnesses in Generalized Quasivarieties |
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95 | (3) |
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4.6 An Extension of the Lowenheim-Skolem Theorem |
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98 | (3) |
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4.7 A Diagram Version of the Gratzer-Schmidt Theorem |
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101 | (3) |
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4.8 Right 0-Larders from Congruence-Proper Quasivarieties |
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104 | (4) |
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4.9 Relative Critical Points Between Quasivarieties |
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108 | (5) |
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4.10 Strong Congruence-Properness of Certain Finitely Generated Varieties of Algebras |
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113 | (1) |
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4.11 A Potential Use of Larders on Non-regular Cardinals |
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114 | (3) |
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5 Congruence-Permutable, Congruence-Preserving Extensions of Lattices |
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117 | (14) |
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5.1 The Category of Semilattice-Metric Spaces |
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118 | (1) |
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5.2 The Category of All Semilattice-Metric Covers |
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119 | (1) |
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5.3 A Family of Unliftable Squares of Semilattice-Metric Spaces |
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120 | (4) |
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5.4 A Left Larder Involving Algebras and Semilattice-Metric Spaces |
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124 | (2) |
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5.5 CPCP-Retracts and CPCP-Extensions |
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126 | (5) |
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6 Larders from Von Neumann Regular Rings |
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131 | (8) |
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6.1 Ideals of Regular Rings and of Lattices |
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131 | (5) |
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6.2 Right Larders from Regular Rings |
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136 | (3) |
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139 | (4) |
| References |
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143 | (3) |
| List of Figures |
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146 | (3) |
| Symbol Index |
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149 | (4) |
| Subject Index |
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153 | (4) |
| Author Index |
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157 | |
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