Abstract logic
Formal system in mathematical logic
In mathematical logic, an abstract logic is a formal system consisting of a class of sentences and a satisfaction relation with specific properties related to occurrence, expansion, isomorphism, renaming and quantification.[1]
Based on Lindström's characterization, first-order logic is, up to equivalence, the only abstract logic that is countably compact and has Löwenheim number ω.[2]
See also
- Abstract algebraic logic – Study of the algebraization of deductive systems, based on the Lindenbaum–Tarski algebra
- Abstract model theory
- Löwenheim number – Smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds
- Lindström's theorem – Theorem in mathematical logic
- Universal logic – Subfield of logic that studies the features common to all logical systems
References
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Mathematical logic
- Axiom
- list
- Cardinality
- First-order logic
- Formal proof
- Formal semantics
- Foundations of mathematics
- Information theory
- Lemma
- Logical consequence
- Model
- Theorem
- Theory
- Type theory
and paradoxes
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Propositional | |
Predicate |
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Types of sets |
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Maps and cardinality |
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Set theories |
language and syntax
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Example axiomatic systems (list) |
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- Interpretation
- function
- of models
- Model
- equivalence
- finite
- saturated
- spectrum
- submodel
- Non-standard model
- Diagram
- Categorical theory
- Model complete theory
- Satisfiability
- Semantics of logic
- Strength
- Theories of truth
- T-schema
- Transfer principle
- Truth predicate
- Truth value
- Type
- Ultraproduct
- Validity
Mathematics portal
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