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A First Course in Mathematical Logic and Set Theory by Michael L. O'Leary

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INDEX

Abel, Niels, 342

Abelian group, 342

Absolute value, 116

Abstraction, 122

Addition, inference rule, 25

Addition, matrix, 355

Additive identity, 199, 412

Additive inverse, 199

Aleph, 313

Algebraic, 315

Alphabet, 5

first-order, 68

second-order, 73

And, 4

Antecedent, 4

Antichain, 183

Antisymmetric, 177

Arbitrary, 88

Argument form, 21

Assignment, 7

Associative, 34, 139, 199, 412

Assumption, 46

Asymmetric, 177

Atom, 3, 6

Automorphism, 380

Axiom scheme, 228

Axiom(s), 24

choice, 231, 235

empty set, 227

equality, 226

extensionality, 227

foundation, 234

Frege–Łukasiewicz, 24

group, 340

paring, 228

power set, 228

regularity, 234

replacement, 230

ring, 353

separation, 228

subset, 229

union, 228

Zermelo, 231

Axiomatizable, finitely, 409

Basis case, 258

Bernstein, Felix, 301

Beth, 316

Biconditional, 5

Biconditional proof, 107

Bijection, 211

Binary, 68

function, 189

operation, 198

relation, 161

Binomial coefficient, 263

Binomial theorem, 263

Boole, George, 117

Bound

lower, 181

upper, 180

Bound occurrence, 77

Burali-Forti paradox, 297

Burali-Forti theorem, 292

Cancellation, 248, 256, 414

Candidate, 99

Cantor–Schröder–Bernstein theorem, 301

Cantor, Georg, 117, 226, 229, 303, 313

Cardinal, 307

large, 332

limit, 314

regular, 328

singular, 328

strongly inaccessible, 332

successor, 314

weakly inaccessible, 331

Cardinality, 308

Cartesian n-space, 131

Cartesian plane, 130

Cartesian product, 130

Cases, 112

Chain, 182

elementary, 394

of structures, 372

Characteristic function, 304

Choice axiom, ...

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