2000 | Introduction to the Theory of Logic |
§1.2 | p.4 | 10886 | Determinacy: an object is either in a set, or it isn't |
§1.3 | p.5 | 10887 | Specification: Determinate totals of objects always make a set |
§1.3 | p.6 | 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) |
§1.6 | p.20 | 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element |
§1.6 | p.23 | 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive |
§2.3 | p.48 | 10891 | If a set is defined by induction, then proof by induction can be applied to it |
§2.4 | p.50 | 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another |
§2.4 | p.51 | 10893 | Γ |= φ for sentences if φ is true when all of Γ is true |
§2.4 | p.53 | 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true |
§2.4 | p.53 | 10895 | 'Logically true' (|= φ) is true for every truth-assignment |
§2.8 | p.71 | 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → |
§3.2 | p.89 | 10897 | A first-order 'sentence' is a formula with no free variables |
§3.3 | p.90 | 10898 | The semantics shows how truth values depend on instantiations of properties and relations |
§3.5 | p.102 | 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations |
§3.5 | p.106 | 10900 | Logically true sentences are true in all structures |
§3.5 | p.106 | 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true |
§3.6 | p.109 | 10902 | We can do semantics by looking at given propositions, or by building new ones |
§3.6 | p.110 | 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model |