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Ideas of Michal Walicki, by Text
[Norwegian, fl. 2012, At the University of Bergen, Norway.]
2012

Introduction to Mathematical Logic

History B.4

p.13

17742

Scotus based modality on semantic consistency, instead of on what the future could allow

History E.1.3

p.33

17747

A 'model' of a theory specifies interpreting a language in a domain to make all theorems true

History E.2

p.34

17748

The LS Theorem says no theory (even of reals) says more than a natural number theory

History E.2.1

p.35

17749

Post proved the consistency of propositional logic in 1921

History Intro

p.2

17741

To determine the patterns in logic, one must identify its 'building blocks'

1.1

p.45

17752

The empty set is useful for defining sets by properties, when the members are not yet known

1.1

p.45

17753

The empty set avoids having to take special precautions in case members vanish

2.1.1

p.69

17754

Inductive proof depends on the choice of the ordering

2.3

p.88

17755

Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals

2.3

p.88

17756

The union of finite ordinals is the first 'limit ordinal'; 2ω is the second...

2.3

p.89

17760

Two infinite ordinals can represent a single infinite cardinal

2.3

p.89

17758

Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion

2.3

p.89

17757

Members of ordinals are ordinals, and also subsets of ordinals

2.3

p.89

17759

Ordinals play the central role in set theory, providing the model of wellordering

4.1

p.118

17761

A compact axiomatisation makes it possible to understand a field as a whole

4.1

p.122

17763

Axiomatic systems are purely syntactic, and do not presuppose any interpretation

4.1

p.122

17762

In nonEuclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate

5.1

p.143

17764

Boolean connectives are interpreted as functions on the set {1,0}

7 Intro

p.183

17765

Propositional language can only relate statements as the same or as different
