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Elementary definition

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while still being expressive enough to support most everyday mathematics (via the addition of elementarily-expressible axioms such as
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Saying that a definition is elementary is a weaker condition than saying it is
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Sheaves in Geometry and Logic: A First Introduction to Topos Theory,
39:. Elementary definitions are of particular interest because they 104: 124: 8: 24:is a definition that can be made using only 131: 117: 31:, and in particular without reference to 7: 85: 83: 14: 87: 41:admit a complete proof apparatus 1: 103:. You can help Knowledge by 35:or using extensions such as 45:Zermelo–Fraenkel set theory 171: 82: 150:Mathematical logic stubs 75:Mac Lane and Moerdijk, 99:-related article is a 37:plural quantification 22:elementary definition 155:Mathematical logic 97:mathematical logic 18:mathematical logic 112: 111: 64:Elementary theory 29:first-order logic 162: 133: 126: 119: 91: 84: 170: 169: 165: 164: 163: 161: 160: 159: 140: 139: 138: 137: 72: 60: 12: 11: 5: 168: 166: 158: 157: 152: 142: 141: 136: 135: 128: 121: 113: 110: 109: 92: 81: 80: 71: 68: 67: 66: 59: 56: 13: 10: 9: 6: 4: 3: 2: 167: 156: 153: 151: 148: 147: 145: 134: 129: 127: 122: 120: 115: 114: 108: 106: 102: 98: 93: 90: 86: 78: 74: 73: 69: 65: 62: 61: 57: 55: 53: 48: 46: 42: 38: 34: 30: 27: 23: 19: 105:expanding it 94: 76: 49: 21: 15: 144:Categories 70:References 33:set theory 52:algebraic 47:(ZFC)). 26:finitary 79:page 4. 58:Related 95:This 20:, an 101:stub 16:In 146:: 54:. 132:e 125:t 118:v 107:.

Index

mathematical logic
finitary
first-order logic
set theory
plural quantification
admit a complete proof apparatus
Zermelo–Fraenkel set theory
algebraic
Elementary theory
Stub icon
mathematical logic
stub
expanding it
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e
Categories
Mathematical logic stubs
Mathematical logic

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