Combining Philosophers
Ideas for Eucleides, Marcus Rossberg and Feferman / Feferman
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17 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751
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Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
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10757
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Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
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10759
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There are at least seven possible systems of semantics for second-order logic [Rossberg]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753
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Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752
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Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754
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In proof-theory, logical form is shown by the logical constants [Rossberg]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158
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A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
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10162
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Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
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10756
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A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758
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If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160
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Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
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10159
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Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
10161
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If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
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10761
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Completeness can always be achieved by cunning model-design [Rossberg]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755
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A deductive system is only incomplete with respect to a formal semantics [Rossberg]
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5. Theory of Logic / K. Features of Logics / 7. Decidability
10156
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'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
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10155
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Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
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