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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 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true
§3.5 p.106 Logically true sentences are true in all structures
§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