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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

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