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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 L-S 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 E.2.2 p.36 17751 Gödel proved the completeness of first order predicate logic in 1930
 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 17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second...
 2.3 p.88 17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals
 2.3 p.89 17757 Members of ordinals are ordinals, and also subsets of ordinals
 2.3 p.89 17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion
 2.3 p.89 17760 Two infinite ordinals can represent a single infinite cardinal
 2.3 p.89 17759 Ordinals play the central role in set theory, providing the model of well-ordering
 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 non-Euclidean 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