Książka - szczegóły

CONTENTS
Introduction............................................................................................................... 3
CHAPTER I. Operations
§ 1. Definition of operation........................................................................................ 6
§ 2. Homomorphisms of operations.......................................................................... 6
§ 3. Congruences of operations................................................................................ 8
§ 4. Direct product of operations............................................................................... 7
CHAPTER II. Abstract algebras
§ 1. Definition of algebra......................................................................................... 10
§ 2. Subalgebras and sets of generators................................................................ 10
§ 3. Borel-classes of elements in algebras............................................................. 12
§ 4. Powers of subalgebras.................................................................................... 13
§ 5. Homomorphisms and congruences of algebras.............................................. 15
§ 6. Direct product of algebras................................................................................ 18
§ 7. $\[\mathfrak{A}\]$-free algebras....................................................................... 20
CHAPTER III. Equationally definable classes of algebras
§ 1. Absolutely free algebra..................................................................................... 21
§ 2. Terms and equations........................................................................................ 25
§ 3. Validity of an equation...................................................................................... 27
§ 4. Validity in subalgebras..................................................................................... 33
§ 5. Validity and homomorphisms........................................................................... 34
§ 6. Validity in direct, products of algebras.............................................................. 35
§ 7. Definition of an equationally definable class of algebras.................................. 36
§ 8. Free algebras in equationally definable classes of algebras............................ 37
§ 9. The characterizations of equationally definable classes of algebras............... 40
APPENDIX TO CHAPTER III. Functionally free algebras....................................... 46
CHAPTER IV. Gödel’s theorem for O-systems
§ 1. O-formulae....................................................................................................... 49
§ 2. The operations of consequence....................................................................... 50
§ 3. Validity.............................................................................................................. 54
§ 4. Lindenbaum model........................................................................................... 58
§ 5. Gödel’s theorem............................................................................................... 59
References.............................................................................................................. 66