INDEX

ADDITIVE, 41, 101

Algebra, 10, 23

Arens, R. F., 71

Axiom, 14

BASS, H., 79, 82, 85, 92, 93

Bausch, A. F., 99

Bernays, P., 236

Binary predicate, 174

Birkhoff, G., 71

Boole, G., 10

Boolean algebra, 10

Boolean filter, 62

Boolean ideal, 17

Boolean logic, 18

Boolean mapping, 60

Boolean relation, 53

Boolean space, 51

CANONICAL EXTENSION, 170

Clopen, 51

Closed, 23, 126, 172

Closure operator, 42

Cofinite, 114

Complete, 19, 30, 49, 129, 130

Compression, 137

Consistent, 18, 30, 129

Constant, 25, 63, 76, 101, 143, 173, 246, 252

Contravalid, 30, 130

Copeland, A. H., 265

Cross section, 64, 80

Curry, H. B., 9

Cylindric algebra, 28, 213

DAIGNEAULT, A., 265

Degree, 26, 113, 171, 252

De Morgan, A., 25

Dilation, 137

Direct image, 52

Discrete quantifier, 41, 100

Domain, 38, 104, 214, 252

Dual algebra, 51

Dual ideal, 17

Dual space, 52

EQUALITY, 216, 255

Equality algebra, 228

Equality homomorphism, 228

Equality model, 228

Equivalence relation, 53

Everett, C. J., 248

Existential quantifier, 22, 40, 100, 170, 243, 251

Extralogical axiom, 16

Extremely disconnected, 81

FALSE, 29, 49, 130

Filter, 17, 62

Finite-dimensional, 114, 214

Finite substitution, 117

Finite transformation, 170, 244

Free algebra, 245

Free monadic extension, 85

Free polyadic algebra, 243

Functional algebra, 76

Functional equality, 219, 256

Functional existential quantifier, 39

Functional monadic algebra, 38, 101, 243

Functional polyadic algebra, 104, 214, 244, 252

Functional quantifier, 243

Functional universal quantifier, 39

Functionally rich, 161, 247

GALLER, B. A., 37, 265

Gleason, A.M., 75, 81, 82

Gödel, K., 31, 169

HEMIMORPHISM, 52, 101

Henkin, L., 9, 99, 136, 166, 228, 47, 261

Hubert, D., 236

Hiz, H., 265

Hochschild, G. P., 11

Homogeneous, 113

Homomorphism, 46, 243, 245

IDEAL, 17, 46, 245

Idempotent, 41, 100, 101

Increasing, 40

Independent, 113, 131, 171, 214, 252

Independent function, 88

Individual variable, 26

Interpretation, 29, 49, 130, 243, 246

Invalid, 49, 130

Inverse image, 53

JONSSON, B., 9, 54, 72, 164, 230

KAPLANSKY, I., 71

K ernel, 245

K ruse, A. H., 37

K uratowski, C, 21

LEBLANC, L., 78, 239, 265

Lewis, C. I., 75

Locally finite, 27, 114, 171, 252

Logic, 18, 49

Logical closure, 284

MAUTNER, F. I., 248

Maximal ideal, 47, 101, 128, 245

McKinsey, J. C. C, 43, 72

Michael, E. A., 75, 82

Model, 29, 49, 130, 246

Modus ponens, 14, 17

Monadic algebra, 23, 46, 101, 243

Monadic filter, 62

Monadic functional calculus, 23

Monadic homomorphism, 46, 101

Monadic ideal, 46, 101

Monadic logic, 49

Monadic subalgebra, 46, 101

Monotone, 41, 52, 100

Monteiro, A., 77

NORMALIZED, 40

OPERATION, 202

PERMUTATION, 131, 170

Polyadic algebra, 27, 111, 171, 245, 251

Polyadic Boolean algebra, 261

Polyadic homomorphism, 125

Polyadic ideal, 126

Polyadic logic, 28, 128, 245

Polyadic subalgebra, 125

Predicate, 173, 252

Proposition, 14, 102, 172, 243

Propositional calculus, 13

Propositional function, 38, 102, 243

Provable, 16, 49

QUANTIFIER, 22, 40, 100, 170, 243, 251, 261

Quantifier algebra, 26

Quasi-multiplicative, 40

Quasi-polyadic algebra, 120

Quotient algebra, 128

RASIOWA, H., 9, 99, 142, 166 247, 248, 261

Reduced equality, 227

Reflexive, 215, 255

Refutable, 49

Relation, 52

Relative product, 53

Relatively complete, 45

Replacement, 131

Retraction, 131

Rich algebra, 66, 77, 155, 246

Rich extension, 66, 155

Rule of inference, 14

SATISFIABLE, 30

Scott, D., 93

Semantic, 19

Semantically consistent, 30

Semantically complete, 49, 130, 243, 246

Semisimple, 31, 50, 101, 128, 243, 248

Sentential calculus, 13

Shepherdson, J., 261

Sikorski, R., 9, 66, 72, 75, 82, 99, 136, 142, 166, 247, 248, 261

Simple algebra, 19, 47, 101, 127, 245

Simple quantifier, 41, 100

Simply complete, 19, 129, 245

Simply consistent, 19, 129, 245

Single-valued predicate, 237, 257

Standard model, 228

Stone, M. H., 37, 72, 265

Subalgebra, 46, 245

Subdirect sum, 31

Submultiplicative, 52

Substitution, 104

Substitutive, 215, 255

Support, 114, 116, 121, 171, 214, 252

Syllogism, 24

Symmetric, 216, 255

Syntactic, 19

TARSKI, A., 9, 28, 37, 40, 43, 54, 72, 75, 92, 99, 166, 213, 230, 243, 247, 248, 261

Tautology, 13

Term, 178, 253

Thompson, F. B., 40, 72, 166, 213, 243, 248, 261

Transformation, 104, 169

Transformation algebra, 27

Transitive, 216, 255

Transposition, 131, 170

True, 29, 49

ULAM, S., 248

Unary predicate, 174

Universal quantifier, 22, 40, 243

Universally invalid, 49, 130, 243

Universally valid, 49

VALID, 30, 49

Value algebra, 38

Variable, 26, 104, 245, 252

Varsavsky, O., 77, 82

WANG, H., 166

Witness, 66, 154

Wright, F.B., 81, 87, 265