Logic as Algebra

Title page
What is logic?
	1. To count or to think
	2. A small alphabet
	3. A small grammar
	4. A small logic
	5. What is truth?
	6. Motivation of the small language
	7. All mathematics
Propositional calculus
	8. Propositional symbols
	9. Propositional abbreviations
	10. Polish notation
	11. Language as an algebra
	12. Concatenation
	13. Theorem schemata
	14. Formal proofs
	15. Entailment
	16. Logical equivalence
	17. Conjunction
	18. Algebraic identities
Boolean algebra
	19. Equivalence classes
	20. Interpretations
	21. Consistency and Boolean algebra
	22. Duality and commutativity
	23. Properties of Boolean algebras
	24. Subtraction
	25. Examples of Boolean algebras
Boolean universal algebra
	26. Subalgebras
	27. Homomorphisms
	28. Examples of homomorphisms
	29. Free algebras
	30. Kernels and ideals
	31. Maximal ideals
	32. Homomorphism theorem
	33. Consequences
	34. Representation theorem
Logic via algebra
	35. Pre-Boolean algebras
	36. Substitution rule
	37. Boolean logics
	38. Algebra of the propositional calculus
	39. Algebra of proof and consequence
Lattices and infinite operations
	40. Lattices
	41. Non-distributive lattices
	42. Infinite operations
Monadic predicate calculus
	43. Propositional functions
	44. Finite functions
	45. Functional monadic algebras
	46. Functional quantifiers
	47. Properties of quantifiers
	48. Monadic algebras
	49. Free monadic algebras
	50. Modal logics
	51. Monadic logics
	52. Syllogisms
Index