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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 Scotus based modality on semantic consistency, instead of on what the future could allow
History E.1.3 p.33 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true
History E.2 p.34 The L-S Theorem says no theory (even of reals) says more than a natural number theory
History E.2.1 p.35 Post proved the consistency of propositional logic in 1921
History E.2.2 p.36 Gödel proved the completeness of first order predicate logic in 1930
History Intro p.2 To determine the patterns in logic, one must identify its 'building blocks'
1.1 p.45 The empty set is useful for defining sets by properties, when the members are not yet known
1.1 p.45 The empty set avoids having to take special precautions in case members vanish
2.1.1 p.69 Inductive proof depends on the choice of the ordering
2.3 p.88 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second...
2.3 p.88 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals
2.3 p.89 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion
2.3 p.89 Two infinite ordinals can represent a single infinite cardinal
2.3 p.89 Members of ordinals are ordinals, and also subsets of ordinals
2.3 p.89 Ordinals play the central role in set theory, providing the model of well-ordering
4.1 p.118 A compact axiomatisation makes it possible to understand a field as a whole
4.1 p.122 Axiomatic systems are purely syntactic, and do not presuppose any interpretation
4.1 p.122 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate
5.1 p.143 Boolean connectives are interpreted as functions on the set {1,0}
7 Intro p.183 Propositional language can only relate statements as the same or as different