Data Portal @ linkeddatafragments.org

Matches in Harvard for { <http://id.lib.harvard.edu/aleph/001419880/catalog> ?p ?o. }

• catalog contributor b2013870.
• catalog created "1965.".
• catalog date "1965".
• catalog date "1965.".
• catalog dateCopyrighted "1965.".
• catalog description "Bibliography: p. 227-241.".
• catalog description "I. On the use of variables : 1. Constants and variables ; 2. Expressions of sentences by means of variables-universal and existential sentences ; 3. Formation of sentences by means of variables-universal and existential sentences ; 4. Universal and existential qualifiers-free and bound variables ; 5. The importance of variables in mathematics".
• catalog description "II. On the sentential calculus : 6. Logical constants-the old and new logic ; 7. Sentential calculus-negation of a sentence, conjunction, and disjunction of sentences ; 8. Implication or conditional sentence-implication in material meaning ; 9. the use of implication in mathematics ; 10. Equivalence of sentences ; 11. The formulation of definitions and its rules ; 12. Laws of sentential calculus ; 13. Symbolism of sentential calculus-truth functions and truth tables ; 14. Application of laws of sentential calculus in inference ; 15. Rules of inference, complete proofs".
• catalog description "III. On the theory of identity : 16. Logical concepts outside sentential calculus-concept of identity ; 17. Fundamental laws of the theory of identity ; 18. Identity of things and identity of their designations-use of quotation marks ; 19. Equality in arithmetic and geometry, and its relationship to logical identity ; 20. Numerical quantifiers".
• catalog description "IV. On the theory of classes : 21. Classes and their elements ; 22. Classes and sentential functions with one free variable ; 23. Universal class and null class ; 24. Fundamental relations among classes ; 25. Operations on classes ; 26. Equinumerous classes, cardinal number of a class, finite and infinite classes-arithmetic as part of logic".
• catalog description "IX. Methodological considerations on the constructed theory : 55. Elimination of superfluous axioms in the original axiom system ; 56. Independence of the axioms of the simplified system ; 57. Elimination of superfluous primitive terms and subsequent simplification of the axiom system-concept of an ordered Abelian group ; 58. Further simplification of the axiom system-possible transformations of the system of primitive terms ; 59. Problem of the consistency of the constructed theory ; 60. Problem of the completeness of the constructed theory".
• catalog description "V. On the theory of relations : 27. Relations, their domains and counter-domains-relations and sentential functions with two free variables ; 28. Calculus of relations ; 29. Some properties of relations ; 30. Relations which are reflexive, symmetrical, and transitive ; 31. Ordering relations-examples of other relations ; 32. One-many relations or functions ; 33. One-one relations or biunique functions, and one-to-one correspondences ; 34. Many-termed relations-functions of several variables and operations ; 35. The importance of logic for other sciences".
• catalog description "VI. On the deductive method : 36. Fundamental constituents of a deductive theory-primitive and defined terms, axioms, and theorems ; 37. Model and interpretation of a deductive theory ; 38. Law of deduction-formal character of deductive sciences ; 39. Selection of axioms and primitive terms-their independence ; 40. Formalization of definitions and proofs, formalized deductive theories ; 41. Consistency and completeness of a deductive theory-decision problem ; 42. The widened conception of the methodology of deductive sciences".
• catalog description "VII. Construction of a mathematical theory: laws of order for numbers : 43. Primitive terms of the theory under construction-axioms concerning fundamental relations among numbers ; 44. Laws of irreflexivity for the fundamental relations-indirect proofs ; 45. Further theorems on the fundamental relations ; 46. Other relations among numbers".
• catalog description "VIII. Construction of a mathematical theory: laws of addition and subtraction : 47. Axioms concerning addition-general properties of operations, concepts of a group and of an Abelian group ; 48. Commutative and associative laws for a larger number of summands ; 49. Laws of monotony for addition and their converses ; 50. Closed systems of sentences ; 51. Consequences of the laws of monotony ; 52. Definition of subtraction-inverse operations ; 53. Definition of subtraction ; inverse operations ; 53. Definitions whose definiendum contains the identity sign ; Theorems on subtraction".
• catalog description "X. Extension of the constructed theory: foundations of arithmetic of real numbers : 61. First axiom system of the arithmetic of real numbers ; 62. Closer characterization of the first axiom system-it's methodological advantages and didactical disadvantages ; 63. Second axiom system for the arithmetic of real numbers ; 64. Closer characterization of the second axiom system-concepts of a field and of an ordered field ; 65. Equipollence of the two axiom systems-methodological disadvantages and didactical advantages of the second system.".
• catalog extent "xviii, 252 p.".
• catalog hasFormat "Introduction to logic and to the methodology of deductive sciences.".
• catalog isFormatOf "Introduction to logic and to the methodology of deductive sciences.".
• catalog isPartOf "Galaxy book, GB133".
• catalog issued "1965".
• catalog issued "1965.".
• catalog language "eng".
• catalog language "engpol".
• catalog publisher "New York, Oxford University Press,".
• catalog relation "Introduction to logic and to the methodology of deductive sciences.".
• catalog subject "510.1".
• catalog subject "Arithmetic Foundations.".
• catalog subject "Mathematics Philosophy.".
• catalog subject "QA9 .T28 1965".
• catalog tableOfContents "I. On the use of variables : 1. Constants and variables ; 2. Expressions of sentences by means of variables-universal and existential sentences ; 3. Formation of sentences by means of variables-universal and existential sentences ; 4. Universal and existential qualifiers-free and bound variables ; 5. The importance of variables in mathematics".
• catalog tableOfContents "II. On the sentential calculus : 6. Logical constants-the old and new logic ; 7. Sentential calculus-negation of a sentence, conjunction, and disjunction of sentences ; 8. Implication or conditional sentence-implication in material meaning ; 9. the use of implication in mathematics ; 10. Equivalence of sentences ; 11. The formulation of definitions and its rules ; 12. Laws of sentential calculus ; 13. Symbolism of sentential calculus-truth functions and truth tables ; 14. Application of laws of sentential calculus in inference ; 15. Rules of inference, complete proofs".
• catalog tableOfContents "III. On the theory of identity : 16. Logical concepts outside sentential calculus-concept of identity ; 17. Fundamental laws of the theory of identity ; 18. Identity of things and identity of their designations-use of quotation marks ; 19. Equality in arithmetic and geometry, and its relationship to logical identity ; 20. Numerical quantifiers".
• catalog tableOfContents "IV. On the theory of classes : 21. Classes and their elements ; 22. Classes and sentential functions with one free variable ; 23. Universal class and null class ; 24. Fundamental relations among classes ; 25. Operations on classes ; 26. Equinumerous classes, cardinal number of a class, finite and infinite classes-arithmetic as part of logic".
• catalog tableOfContents "IX. Methodological considerations on the constructed theory : 55. Elimination of superfluous axioms in the original axiom system ; 56. Independence of the axioms of the simplified system ; 57. Elimination of superfluous primitive terms and subsequent simplification of the axiom system-concept of an ordered Abelian group ; 58. Further simplification of the axiom system-possible transformations of the system of primitive terms ; 59. Problem of the consistency of the constructed theory ; 60. Problem of the completeness of the constructed theory".
• catalog tableOfContents "V. On the theory of relations : 27. Relations, their domains and counter-domains-relations and sentential functions with two free variables ; 28. Calculus of relations ; 29. Some properties of relations ; 30. Relations which are reflexive, symmetrical, and transitive ; 31. Ordering relations-examples of other relations ; 32. One-many relations or functions ; 33. One-one relations or biunique functions, and one-to-one correspondences ; 34. Many-termed relations-functions of several variables and operations ; 35. The importance of logic for other sciences".
• catalog tableOfContents "VI. On the deductive method : 36. Fundamental constituents of a deductive theory-primitive and defined terms, axioms, and theorems ; 37. Model and interpretation of a deductive theory ; 38. Law of deduction-formal character of deductive sciences ; 39. Selection of axioms and primitive terms-their independence ; 40. Formalization of definitions and proofs, formalized deductive theories ; 41. Consistency and completeness of a deductive theory-decision problem ; 42. The widened conception of the methodology of deductive sciences".
• catalog tableOfContents "VII. Construction of a mathematical theory: laws of order for numbers : 43. Primitive terms of the theory under construction-axioms concerning fundamental relations among numbers ; 44. Laws of irreflexivity for the fundamental relations-indirect proofs ; 45. Further theorems on the fundamental relations ; 46. Other relations among numbers".
• catalog tableOfContents "VIII. Construction of a mathematical theory: laws of addition and subtraction : 47. Axioms concerning addition-general properties of operations, concepts of a group and of an Abelian group ; 48. Commutative and associative laws for a larger number of summands ; 49. Laws of monotony for addition and their converses ; 50. Closed systems of sentences ; 51. Consequences of the laws of monotony ; 52. Definition of subtraction-inverse operations ; 53. Definition of subtraction ; inverse operations ; 53. Definitions whose definiendum contains the identity sign ; Theorems on subtraction".
• catalog tableOfContents "X. Extension of the constructed theory: foundations of arithmetic of real numbers : 61. First axiom system of the arithmetic of real numbers ; 62. Closer characterization of the first axiom system-it's methodological advantages and didactical disadvantages ; 63. Second axiom system for the arithmetic of real numbers ; 64. Closer characterization of the second axiom system-concepts of a field and of an ordered field ; 65. Equipollence of the two axiom systems-methodological disadvantages and didactical advantages of the second system.".
• catalog title "Introduction to logic and to the methodology of deductive sciences. [Translated by Olaf Helmer.".
• catalog type "text".