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Ideas of José L. Zalabardo, by Text

[Spanish, b.1964, Lecturer at the University of Birmingham, then University College, London.]

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