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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 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 10895 'Logically true' (|= φ) is true for every truth-assignment
 §2.4 p.53 10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true
 §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 10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true
 §3.5 p.106 10900 Logically true sentences are true in all structures
 §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