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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