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'Thinking About Mathematics', 'works' and 'Introduction to Mathematical Logic'
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6 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
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Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
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